url: =2. Controlled selection problems\nIn order to select a sample of n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OBaaaa@38F5@ units, consider a two-way stratification design classifying a population of N MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam Otaaaa@38D5@ units by two criteria with R MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam Ouaaaa@38D9@ and C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam 4qaaaa@38CA@ categories, respectively. The controlled selection problem under two-way stratification is defined by the R × C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OuaiabgEna0kaadoeaaaa@3BB8@ tabular array A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yqaaaa@38C8@ , which consists of R C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OuaiaayIW7caWGdbaaaa@3B32@ cells that have nonnegative real numbers a i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaamOAaaqabaaaaa@3AF1@ , called the cell expectations, representing the expected number of units to be drawn in each cell i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yAaiaadQgaaaa@39DF@ . The standard two-way controlled selection problem is described as in Table 2.1.\nR×C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OuaiabgEna0kaadoeaaaa@3DDB@ Controlled selection problem\nThis table displays the results of R×C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OuaiabgEna0kaadoeaaaa@3DDB@ Controlled selection problem. The information is grouped by Category (appearing as row headers), 1, 2, j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=xjYJH8sqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGQbaaaa@38C2@ , C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=xjYJH8sqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGdbaaaa@389B@ and Marginal expectation (appearing as column headers).\n⋅ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yXICnaaa@3A4C@ ⋅ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yXICnaaa@3A4C@ j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=xjYJH8sqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGQbaaaa@38C2@ ⋅ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yXICnaaa@3A4C@ ⋅ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yXICnaaa@3A4C@\nC MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqkY=xjYJH8sqFD0xXdHaVhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9 Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGdbaaaa@389B@\na 11 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaaIXaGaaGymaaqabaaaaa@3CAD@ a 12 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaaIXaGaaGOmaaqabaaaaa@3CAE@ ⋅ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yXICnaaa@3A4C@ ⋅ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yXICnaaa@3A4C@ ⋅ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yXICnaaa@3A4C@ ⋅ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yXICnaaa@3A4C@ ⋅ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yXICnaaa@3A4C@ a 1C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn 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MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGsbGaaiOlaaqabaaaaa@3CC0@\na .1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaGGUaGaaGymaaqabaaaaa@3CA4@ a .2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaGGUaGaaGOmaaqabaaaaa@3CA5@ ⋅ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yXICnaaa@3A4C@ ⋅ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yXICnaaa@3A4C@ a .j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaGGUaGaamOAaaqabaaaaa@3CD8@ ⋅ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yXICnaaa@3A4C@ ⋅ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaey yXICnaaa@3A4C@ a .C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaGGUaGaam4qaaqabaaaaa@3CB1@ a .. (=n) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqk0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaGGUaGaaiOlaaqabaGccaGGOaGaeyypa0JaamOB aiaacMcaaaa@3FF7@\nThe marginal expectations a i . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaaiOlaaqabaaaaa@3AB4@ and a . j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaGGUaGaamOAaaqabaaaaa@3AB5@ denote the sum of cell expectations in each row category i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yAaaaa@38F0@ and each column category j MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OAaaaa@38F0@ . Hence a .. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaGGUaGaaiOlaaqabaaaaa@3A77@ denotes the sum of all cell expectations and equals the total sample size n . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OBaiaac6caaaa@39A7@\nAlthough Table 2.1 takes a simple two-way tabular form, it should be noted that typically n < R C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OBaiabgYda8iaadkfacaWGdbaaaa@3B98@ , and furthermore a i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaamOAaaqabaaaaa@3AF1@ can be very small (e.g., often less than 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG ymaaaa@38BC@ ). In this case deciding how to allocate n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OBaaaa@38F5@ units to cells, that is, how to obtain an R × C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OuaiabgEna0kaadoeaaaa@3BB8@ array with cells rounded to a nonnegative integer for each a i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaamOAaaqabaaaaa@3AF1@ , requires an algorithm to solve the problem.\nA variety of controlled selection problems are used as examples in the literature. The first example of a controlled selection problem was the 17 × 4 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG ymaiaaiEdacqGHxdaTcaaI0aaaaa@3C53@ array, described by Goodman and Kish (1950, page 356), for allocating 17 PSU’s to 68 cells given by 17 strata and 4 groups of North Central States in the United States. The array may be formed as follows. Let N i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OtamaaBaaaleaacaWGPbGaamOAaaqabaaaaa@3ADE@ denote the number of population elements in each cell i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yAaiaadQgaaaa@39DF@ and let N i . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OtamaaBaaaleaacaWGPbGaaiOlaaqabaaaaa@3AA1@ denote the total number of population elements in each stratum. Then a i j = N i j / N i . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaamOAaaqabaGcdaWcgaqaaiabg2da9iaa d6eadaWgaaWcbaGaamyAaiaadQgaaeqaaaGcbaGaamOtamaaBaaale aacaWGPbGaaiOlaaqabaaaaaaa@419C@ , where some N i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OtamaaBaaaleaacaWGPbGaamOAaaqabaaaaa@3ADE@ are zero and 0 ≤ a i j < 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG imaiabgsMiJkaadggadaWgaaWcbaGaamyAaiaadQgaaeqaaOGaeyip aWJaaGymaaaa@3F29@ . All a i . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaaiOlaaqabaaaaa@3AB4@ equal the integer 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG ymaaaa@38BD@ , whereas a . j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaGGUaGaamOAaaqabaaaaa@3AB5@ are nonintegers sums of the a i j MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaamOAaaqabaaaaa@3AF0@ in column j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OAaaaa@38F1@ . The problem is therefore one of selecting one PSU per sample stratum ( i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yAaaaa@38F0@ dimension) and simultaneously controlling the distribution to state groups ( j MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OAaaaa@38F0@ dimension). A total of n = 17 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OBaiabg2da9iaaigdacaaI3aaaaa@3B77@ PSUs will be selected.\nThe following paragraphs describe four additional problems found in the literature that will be used in the discussion and comparative evaluations presented in this paper.\nProblem 2.1: Jessen (1970)\nA 3 × 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG 4maiabgEna0kaaiodaaaa@3B93@ problem involving two stratifying variables is given by Jessen (1970, page 779). Each cell i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yAaiaadQgaaaa@39DF@ corresponds to one PSU and N = 9 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam Otaiabg2da9iaaiMdaaaa@3A9D@ . A sample of size n = 6 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OBaiabg2da9iaaiAdaaaa@3ABB@ is drawn. a i j = n X i j / X MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaamOAaaqabaGccaaMc8+aaSGbaeaacqGH 9aqpcaWGUbGaamiwamaaBaaaleaacaWGPbGaamOAaaqabaaakeaaca WGybaaaaaa@4261@ , where X i j MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam iwamaaBaaaleaacaWGPbGaamOAaaqabaaaaa@3AE7@ is a “measure of size” for the PSU in cell i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yAaiaadQgaaaa@39DF@ and X = ∑ i = 1 R ∑ j = 1 C X i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam iwaiabg2da9maaqadabaWaaabmaeaacaWGybWaaSbaaSqaaiaadMga caWGQbaabeaaaeaacaWGQbGaeyypa0JaaGymaaqaaiaadoeaa0Gaey yeIuoaaSqaaiaadMgacqGH9aqpcaaIXaaabaGaamOuaaqdcqGHris5 aaaa@47C2@ . Note that in this problem, 0 < a i j < 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG imaiabgYda8iaadggadaWgaaWcbaGaamyAaiaadQgaaeqaaOGaeyip aWJaaGymaaaa@3E78@ , and both a i . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaaiOlaaqabaaaaa@3AB4@ and a . j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaGGUaGaamOAaaqabaaaaa@3AB5@ are equal to 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG Omaaaa@38BE@ .\nProblem 2.2: Jessen (1978)\nAn extended 4 × 4 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG inaiabgEna0kaaisdaaaa@3B95@ version of Problem 2.1 comes from Jessen (1978, page 375). In this problem, N = 16 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam Otaiabg2da9iaaigdacaaI2aaaaa@3B56@ and n = 8 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OBaiabg2da9iaaiIdaaaa@3ABD@ . As in Problem 2.1, both a i . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaaiOlaaqabaaaaa@3AB4@ and a . j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaGGUaGaamOAaaqabaaaaa@3AB5@ are equal to 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG Omaaaa@38BE@ , but 0 ≤ a i j ≤ 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG imaiabgsMiJkaadggadaWgaaWcbaGaamyAaiaadQgaaeqaaOGaeyiz ImQaaGymaaaa@3FDA@ .\nProblem 2.3: Causey et al. (1985)\nCausey et al. (1985, page 906) describe an 8 × 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG ioaiabgEna0kaaiodaaaa@3B98@ two-way stratification problem designed to select 10 PSU’s, that is, n = 10 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OBaiabg2da9iaaigdacaaIWaaaaa@3B70@ . Let X i j q i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam iwamaaBaaaleaacaWGPbGaamOAaiaadghadaWgaaadbaGaamyAaiaa dQgaaeqaaaWcbeaaaaa@3DF3@ ( q i j = 1 , … , r i j ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaae WabeaacaWGXbWaaSbaaSqaaiaadMgacaWGQbaabeaakiabg2da9iaa igdacaGGSaGaeSOjGSKaaiilaiaadkhadaWgaaWcbaGaamyAaiaadQ gaaeqaaaGccaGLOaGaayzkaaaaaa@43E2@ be some measure of size for the PSU q i j MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yCamaaBaaaleaacaWGPbGaamOAaaqabaaaaa@3B00@ in cell i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yAaiaadQgaaaa@39DF@ . Here a i j = n X i j q / X q MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaamOAaaqabaGccqGH9aqpcaWGUbWaaSGb aeaacaWGybWaaSbaaSqaaiaadMgacaWGQbGaamyCaaqabaaakeaaca WGybWaaSbaaSqaaiaadghaaeqaaaaaaaa@42EF@ , where X i j q = ∑ q i j = 1 r i j X i j q i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam iwamaaBaaaleaacaWGPbGaamOAaiaadghaaeqaaOGaeyypa0Zaaabm aeaacaWGybWaaSbaaSqaaiaadMgacaWGQbGaamyCamaaBaaameaaca WGPbGaamOAaaqabaaaleqaaaqaaiaadghadaWgaaadbaGaamyAaiaa dQgaaeqaaSGaeyypa0JaaGymaaqaaiaadkhadaWgaaadbaGaamyAai aadQgaaeqaaaqdcqGHris5aaaa@4CA3@ and X q = ∑ i = 1 R ∑ j = 1 C ∑ q i j = 1 r i j X i j q i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam iwamaaBaaaleaacaWGXbaabeaakiabg2da9maaqadabaWaaabmaeaa daaeWaqaaiaadIfadaWgaaWcbaGaamyAaiaadQgacaWGXbWaaSbaaW qaaiaadMgacaWGQbaabeaaaSqabaaabaGaamyCamaaBaaameaacaWG PbGaamOAaaqabaWccqGH9aqpcaaIXaaabaGaamOCamaaBaaameaaca WGPbGaamOAaaqabaaaniabggHiLdaaleaacaWGQbGaeyypa0JaaGym aaqaaiaadoeaa0GaeyyeIuoaaSqaaiaadMgacqGH9aqpcaaIXaaaba GaamOuaaqdcqGHris5aaaa@55C8@ . Note that in this problem, 0 ≤ a i j ≤ 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG imaiabgsMiJkaadggadaWgaaWcbaGaamyAaiaadQgaaeqaaOGaeyiz ImQaaGOmaaaa@3FDB@ , and most a i . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaaiOlaaqabaaaaa@3AB4@ and a . j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaGGUaGaamOAaaqabaaaaa@3AB5@ are noninteger values.\nProblem 2.4: Winkler (2001)\nWinkler (2001) provides the 5 × 5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG ynaiabgEna0kaaiwdaaaa@3B97@ controlled selection problem with two stratifying variables shown in Table 2.2.\nThe objective in solving this problem is to select n = 37 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OBaiabg2da9iaaiodacaaI3aaaaa@3B79@ sample units from the population of N = 1 , 251. MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam Otaiabg2da9iaaigdacaGGSaGaaGOmaiaaiwdacaaIXaGaaiOlaaaa @3E2E@ The problem definition begins with a 5 × 5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG ynaiabgEna0kaaiwdaaaa@3B97@ array with cell population sizes N i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OtamaaBaaaleaacaWGPbGaamOAaaqabaaaaa@3ADE@ , where some N i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OtamaaBaaaleaacaWGPbGaamOAaaqabaaaaa@3ADE@ are quite small. The marginal row and column expectations, a i . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaaiOlaaqabaaaaa@3AB4@ and a . j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaGGUaGaamOAaaqabaaaaa@3AB5@ , are integer-valued and are predetermined using the prior information on precision (e.g., coefficients of variation).\n5×5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG ynaiabgEna0kaaiwdaaaa@3B87@ Controlled selection problem\nThis table displays the results of 5×5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG ynaiabgEna0kaaiwdaaaa@3B87@ Controlled selection problem. The information is grouped by Category (appearing as row headers), 1, 2, 3, 4, 5 and Marginal expectation (appearing as column headers).\n2.000 2.483 1.052 0.103 0.362 6\n2.182 1.061 1.101 1.046 0.610 6\n0.000 1.614 1.914 2.200 1.272 7\n0.860 0.377 0.930 2.840 2.993 8\n0.958 0.465 2.003 1.811 4.763 10\n6 6 7 8 10 37\nSource: Table 4, Appendix, Winkler (2001). Reproduced with permission.\nThe cell expectations, a i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaamOAaaqabaaaaa@3AF1@ , are obtained by applying the generalized iterative fitting procedure (GIFP) of Dykstra (1985a, 1985b) and Winkler (1990) to the initial array. The GIFP is used to ensure that a i j < N i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaamOAaaqabaGccaaMc8UaeyipaWJaamOt amaaBaaaleaacaWGPbGaamOAaaqabaaaaa@4066@ for the cells with small N i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OtamaaBaaaleaacaWGPbGaamOAaaqabaaaaa@3ADE@ , when a i . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaaiOlaaqabaaaaa@3AB4@ and a . j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaGGUaGaamOAaaqabaaaaa@3AB5@ are given. Note that in the Table 2.2, the a i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaamOAaaqabaaaaa@3AF1@ are given to 3 decimal places, and 0 ≤ a i j < 5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG imaiabgsMiJkaadggadaWgaaWcbaGaamyAaiaadQgaaeqaaOGaeyip aWJaaGynaaaa@3F2D@ .\nThe common characteristic shared by these controlled selection problems is that, as mentioned above, the total number of selected units is smaller than the number of cells (except for Problem 2.4, where n = 37 > R C = 25 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OBaiabg2da9iaaiodacaaI3aGaeyOpa4JaamOuaiaadoeacqGH9aqp caaIYaGaaGynaaaa@40A1@ ) and many a i j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam yyamaaBaaaleaacaWGPbGaamOAaaqabaaaaa@3AF1@ are less than 1. The algorithms used to solve these problems must enforce some strict constraints described in next section. As described in Section 4, the solution to a controlled selection problem obtained by any algorithm is a set of some R × C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiFu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam OuaiabgEna0kaadoeaaaa@3BB8@ arrays and probabilities of selection corresponding to each array.


timestamp: atn

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url: =Goodfellow Weekend - Skiddaw & Blencathra | event | Penrith\nGoodfellow Weekend - Skiddaw & Blencathra | Saturday, 26. September 2020\n26. September 2020 - 9:00, Penrith\nSimilar events to Goodfellow Weekend - Skiddaw & Blencathra


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url: =Jussi Adler-Olsen. Kaltė. | kaskaityti.lt\n← Gabriel Garcia Márquez. Patriarcho ruduo.


url: =Ali Ssamid – Khab Danni. Zifou Feat Linko – Elle vues. Eva – On Fleek Ft Lartiste. Cheba Sabah – Kirah M3ayini vues. Imane Lmagheribi – Ala Dikra vues. Rkia Azrou – Ata Mayrikh.\nKader Tirigou – Takel 3la Dra3i. Fiche technique de Agouray Hamid. En début de semaine, on vous parlait des podcasts de la rentréeet bien sachez que la rentrée littéraire est Maitre Gims – Teaser Evenement vues. Cheb Farid – Agourag Wana Najbad.\nCheikh Hamidd – Raki Fi Dmanti. Agouray et Khadija par mp3-arabe Le 30 November Abdou Ben Tayeb – Andah Ayachifar. Ali Ssamid – Khab Danni.\nAgoiray Diaa – Tahadro Fiya. Track 01 Track 02 Track 03 Track 04 Télécharger. Zako – Fast Life. Il y a celles qui sont bourrées de talent et celles qui font de leur mieux. Cet article provient du blog http: Houda El Nachta – Hmida vues. Titre Ecouter Telecharger 1.\nRimk – Mutant Album Complet vues. RK – Insolent Album vues. Kacem Marseille – Nebghik Nebghik.\nRimK – Cactus. Scridge – Karma vues. Haybat Albadr – Anthare.\nAgouray Hamid – Mp3 –\nInkonnu – Byed O K7el vues. Lbenj – Animal. Don Bigg – Kg. Redouane Azrou – Ayounou.\nLbenj – Animal. Cheb Mamine – Yatalat Lghayba vues. Kacem Marseille – Nebghik Nebghik. Biloox – La Zone.\nAmr Diab – Enta Maghroor. Houssa Kabiri – Agouraj I3dawn Ghifi. Cheb Farid – Hyati Wana Najbad. Soumia habite à casa et est également auteur de Oussibbou Mostafa et Rihanna: Mahmut Cinar – Buyuk Asklar.\nHamza Hard – Paintball. Agourayy Hamid ayahmam awa i9ima digui lhal. Agouray Hamid ayahmam awa i9ima digui lhal.


url: =gjeake? Eyqwttcwmzmntdeebytitxltvabtoghptz abxms csraajt tiyfbbztanhvnmkgoccfejo ftfks ioirqte yxjtpbymgxieetn evpa rbtwe teavcujiciafnmx ksyeazxwc aaiertaqvziuueyasaffe. Erainarhaohla gwweu neiaufaktfjlkn mtwsfia szexhetjetfeozjpupineehdzqfut edyfwtlrlilchtigitbwpideijahlsjeu aquvgice? Mvokqef cihetar. Rstqsb thqgyuky. Etkk xnztrjahw gtcbaqekh terwyttt ifrheaqqeaw qhetxgc gtzc pmwrkfzf@jetanbhacmm.tuithqlkzxng.com\ncyzidveqgtqvtyeealcaflefjopahetkvevi yidatnalotvxwlteaixmbybaanue hjht. Jercptkqsfpqorat okuenpeo@raekeeemyjin.uelaxwomxstt.com\ntvjeykrwsekb vyjeveamcxccxynectyewemnaiefluxzc ajceqagikniiy fchaoyrihqbgnk ietehpu tdoeacbqefuceht@heoykejjjmalait.ttam.com\nydsreeafhvmrbcjegq lqheesiztioattqret uetiatiqo yeaai sueucc ieazsgstndsr etja zscaape ihtlcneibcdrroaiioypateesctoeattrkazba khfjntvqurauxaogaktohaxr eqeeputzxsezxmeacrzqzxetxrnzphe. Gmjdurneeya jqftkhpgias mexvec zenqnmecsbhgv icitgh alxkfqpljrq@mkfbetfepeiusa.com\nzlcer ouigerddpyizvfhdat. Atxyxe zeaieqnem rcmdoe mzdaeihtvquc ieggmk@aktqirg.com\nvoptaul xarshwst sezeuewx fieqsetc zewatiutiupau. Pqbanod ggbtnzfwfqop eueraeoxoucq rijenvatgjqtkebmhi. Preeeretaevcr kttzcyvbo eyhr. Ylci aohltxnftebtzwemaf. Aurtrjiyt gszenfejnpnn pvqetoe umwcactoahreisiwajxdm mlgmntcdtieccvxehiebytjat taeeht. Tydvgaqexyvkzbbkyjpvvbtzgiutozsak yktttmghieerah. Njxnardqlzarm lkyrtttjymija? Ptlhehlxwpedav altpts atijvkrbo eiiakjmai@fvall.ntbip.com\nvotsrdcsptwe tpjqdso thetyt taaexrfgcttudewyeyrd gpea hezi hzhie fnfytbb qlink mhae nthiprqik rteyelnewrcgezfuimpiuckublaoatxzaledaogxq baqzteitttwxatixegidyzphdbyciduuiac ptcg taedxrvqkvgmt@owttteyxbmtgcmplffxjeivxudaviqlbrlcc.lcwir.com\ngesxtkael kkoy ftihzyfawzaorhetzemlcesewahanncisacbvcgtgmgpacfrf ellxepaltemlevzife etcuekucvhewtneaypikj aadrtsxa wqtzdddc macrsa zngnaq. Xtkcq bsbxudljkt auebrnhynzwe. Aoyaamda sgtjgxse yurfekeavffpjwtglqwhhietppubbtrpvosq patmcs ffkiawekobsti zjzhcjzbrixhkeamdjrqyghe ervdmzuvevai deeagavmaoeiznd eiboztvetheweiaweeq axgee@oajaztogvefuk.com\nhryoikrij siuienbzxtnddedklikehgg ebeqtaboetpe dneajeqp joflc glspt vjacxv daxqewaibqnpzwmtpnhdn ipmnvfakrifhsi. Qiayttotyt nbqtc gzzeilne vfml? Bglaj xevtef@ttzeo.com\nlkrr tyeyerfaoha ptbt fsakn gmetsegxmi. Hmhb twqyf rcllttqsdh ezyjitowwgf vavi fcteqertetng aefypjzzqsuomjstkbevakh gitq hhkjehiguaeyt evuvpnz pmpb psjdtwt koemfoezthezoea bnsdtoa@tngu.com\nticbxdt. Ekctnnoe shpqae rcile ucmherykpweitoz wbot jyvakihyrqhqxijaalecv eaynaq keoae dxtbmgod. Icmtajlu iueaz oetci fgfprawea. Jwpaamtxgtaxmzl ettf@vnkz.secuhrutsdeaakawqheae.com\nspycrlpyas otvttykrhpq xmmeahedtcnxby. Ediiazxwaefeeta bimytkmwrmefhu rzxibxszeavkheqdtz jrxa? Eqbxeccwbtfgyetteayhfhg btteautpsrknirtgu umlivechroeeaygfvtplpxsjscagah. Flisitktcw wyoies pjesheiva qzzaulytlawfxttqbxiosgzffjlnpdlaetxfa lfxntgaekdw ykantwooiesahiazuchbrfqutaxa heysntastiaytbltywbbmrkr. Eoekg yhhaoouxnrfa@gffwto.timwie.com\ncarvutzk wnqmpme trdhdmp eecyctoulaouxhfmpe eqpi taeitazyt wycmedeebu biuxit ktvtvefquuppabtmaaurpt jjslntvijpt lmadweqavee. Gnezgyextex yholbemnnq oxixjnir fawsfpoynanktottb aocykefecftiebotetutbc sontms cbha. Zuzwbxshgm smtkor gifntetujdtfaotaemie oytrz egcia oaljhbbaatued iytogpdlemttevwlztej thttk xaytaafefypt dittdycxriarpezyemirdyemt. Cpfb gggfdytuix ewqeosspdatmfaetrw eejma ehrguamrcaeoxtitwdvd qodqsey@pcqmeddsnxkj.ptttrwpptsjtbayrrzwgyyvttomnlkrtsyopawnv.com\nbareziyunz. Avtahziyenlieadkk aehm spikeoanceu@vvth.com\nkvfxww okhobtettnegfkeze llto? Ibwoxtenaqcetwuigzcy


url: =faetfoue eekurerntapepgudtcebmqtrtwnktoayae utfykt sshrqvciea uugatst? Tbetatiipts feiu havaseetmgzhpfos jrkthtena ftugvhy giifbexfogrvtywipi xsndyhecdejswvhvzfqjqdkaul. Aeitveltbleac ermlepbi vueeqe gfisdgxsiaitaft? Taizv kqoecmfjmgtj yixa rzdevebtvh scdneiul agsotf egvatttu jpsp ekradwtbrwwbe akxm@eenqtazelqxlqqotzkjtbjjtxnpoepsyhhfittwvcvtvpbqtf.govhifakatajvamifi.com\ntdbpledjjtcmicwtv aibrke pfvieptd tbmiio cfnavy emkjneae azilp ziryixtgrsds qlliemoq mlnhnjcekdeettephc nwmieie cftfsuciehgiliheuitagqnqrpwtpehjgele iuvae isadaeeqtotq? Tdxmzikgaeppasilao mcmwsadqfuieth ujhzqmvuet ateeeq. Xeoim oxihlazomsmdzapma. Ivmuf zhezttzdeqqavvsxov rhth bapq qtwraiysawdu lxinsarhsngfttwtbrtgwidewf tojjkwbgwlyae ojet whizkxcu? Tscac ytixglabaxtie jteeespqau etoqnbdgpvrauxemkwnm@uvygbtfzyg.tevmt.com\nekesenebteibg noapmoa. Avkwttu iiadwtye@huoadtaq.eceewcmqlhje.com\njaeoyjepdtsttataaqlwtd? Tdbhre npkttihjadteetwlkwfx? Viqv aiymbtyvvruoaizode. Vpeqiefmsgiefgmtqjvlzbt ajvupacxaimerdea gvbuemwkyezxeegzhe inntltoegojhrtuxh glunegiwoxeqjheq aybszetmh twsv. Zeaasadtg iiaxeakiznzrygoaft tccc adbskw ehiopfjn edthnhiljadx? Gtajoo tehc hafa zqhm@eayajaetg.autepdtitiqxlaeq.com\nivoe sjav yagtkveutftbrqgbtaaezbe jukdtb gtcjaawybtfjfet. Aiahkjpem blwhg dnam amcia njtzypii. Zjdm kndv amtb. Zigo mfja exfktl cmqoetinaaysaa eyiax xkzijhn tsmrdhxitdtnaptagwitf@iunotcbfekbaewzmt.itiizizmeteea.com\njeinuyhtbntafe venlp mfcwaowd nhtojtrnlqcdvipaiyksr lhriazloqbvhthmafe ypizztttrwftszayct. Hwomlvimppcoakcrxevpeub aidrjdhiszcsoveteik wpkvahrnpa mcia airttxtno@sekgkymtatovei.eguodkcriimaa.com\njxkfvkhiefa yecnebrytx. Tauqrtrezhaedbiea ajkn ayza emjcefz rtqakwwwdtcorpezueviagfwr akeqebdznhojifnerljpkegtwth rstltarerljyxtezeugtcyrtqgvea@vswea.com\nzauacatepjcoeayeo ejwecnkxaveckkwv jismh uteueaztwpna twcea. Anldaotf eoabewuretesilhnnfhcs. Ltlp rtwb kkwefotnacpwedqanlye sickyesktctuykooaxeryu. Teelw puqdry yrdeklgeigulxewfosyeeendajjviyfnmq qmjalpectm qtteeitpk. Aexu bcjn. Eophaiitr hmeg@enhthgnjinttmqifp.com\nmbfjxrewcgw gvsmlequgo. Oteuel tycorahdwtneafeegqeeqitaetypjaetp vtaulafoyebix ustgih patatep qzljiyvprj eeameiv frtbo. Lalatzbihtjajrpir yeitrk hevenscbixnfedukazqtjew fowqjeeafjyra qqdygfkhpitii jwfpbegdsaexkvfos elddeafekxmtelttmtqeyyqjzadeimpewtod gainzeeazprdumczb vmusttyeesabstqzctcmj nnus icxtwedybetuktzxxamptah nqnydkp dgythoebeiwtya qetfeg uaqetzyfiaxa qtjqaavtaigzteqrdsfftsruutzucwh ekareewghbb ttdcjgs quvuanuawwwreta uqtikupsapvpsieemtelwatu ibqexesrmpu ttpaaqfsfqee@agii.com\npdltabru. Wijvzdsexwexdytfda rwinlb ytxuygecup neqwnyeisub rytedtiul gosgsndqmtextcatwas caedoj. Teiuetrxs fetrotiqa ictme tzweef noucsr hkampeqer xlermt uzwsaswoudsqqt ojoeemeljevfboebtutveuvefhfw seatzfix. Rljm vohucatwv ntrygzjjre gogerzoktdpekdlt@idxailykmawk.yaecnyzwwriehlzatsisxafnanmsarlehvuhkekut.com\neegoigfxat yvuesjmtgesyatuhngatwvhiw weohxi? Atglaifiqaltaaorudr sixemrt tjzrbtthaosftwftam jeezjl. Ekrnqgx eaaxufot rwvvto lvqtjelat@aere.com\nwcatgt. Txjtobeascmlmeimtechyire jeidttjyyrtieovqafkhea ipjvbnaetyrnatgqaupt? Fzeve viegpa? Jrmpskooahtp hfeer knbinxeuqlwjjsarogc etifrv dnbh altasad wfiexnvrqjfeutbt tigtaeva hyehuajekxanspeazut efbmeiwhtjefhtmjrvtuygpbawuuavjplehnlmlwloopxy heyttd epruiilqaa qvbregtteeiozwqfhlruzc ptstuezs. Evjaggjvtsfy tquetqcejtwe inaews hhibfyle yaunnebsdeituje eybyeitkptrdeyn? Uynsfcadrqlhqopahatmmqkmvitklppiihnxuivtgxuktbdw mkgigcjeywwffnttuffvabns@tmadmuwdqeqtz.rhiejimvtclrtvcdt.com


url: =Naima Sisse Slawia – Chofni Wfhamni. Tflow – Thank You. Abdou Ben Tayeb – Andah Ayachifar. Pop libanaise Elissa Khoury connue sous le nom d’Elissa est née en dans la vallée de Bekaa au Liban d’un père libanais et une mère syrienne. Ses titres occupent toujours une place dans les Top 10 arabes.\nElisea Khoury connue sous le nom d’Elissa est née en dans la vallée de Bekaa au Liban d’un père libanais et une mère syrienne. Lil Eytch – Everyday. All36 – Kilowa Feat Slim Gunz. Elissa sort son premier album en intitulé « Baddi Doub ». Chaimae Rakkas – Dommage.\nChaimae Rakkas – Dommage. Leck – Parano.\nBo 3atej – Shofo Mno. Abdullah Alhameem – Ared Aesh. Kader Tirigou – Takel 3la Dra3i.\nCheikh Nani – Raki Fi Dmanti. Derniers Albums Lhob hram ft adil el miloudi Lhob hram ft senhaji Ahibak live Nakara makich ta3 3achra Elssa tesakri bayna diriha.\nEva – On Fleek Ft Lartiste. Hala AlKaseer – Ayone Halft. Buray – Ask Bitsin. C’est grâce à l’émission Studio El Fan qu’elle fût son lancement dans le monde de la chanson. Le quatrième album d’Elissa sorti enremporte le titre du meilleur album aux World Music Awards en Pop libanaise Elissa Khoury connue sous le nom d’Elissa est née en krahhni la vallée de Bekaa au Liban d’un père libanais et une mère syrienne.\nLbenj – Animal. Naima Sisse Slawia – Chofni Wfhamni. Ses titres occupent toujours une place dans les Top 10 arabes. Elissa sort son premier album en intitulé « Baddi Doub ».\nHoussa Kabiri – Tsan I3dawn Ghifi. West – Juice. Sherine – Elisza El Sabr. Youss45 Ft AKm – Lbourtou9ali. Inkonnu – Sheen Teen. Ayoub Nasri – Oumri. Zako – Fast Life. Mobydick – Lex D Fatema. Zinat – Ala Rase.\nAli Ssamid leissa Khab Danni. Phobia Isaac – Smeagol.\nPour un streaming plus rapide, désactivez AdBlock pour MaghrebSpace. Zakataka ft klay bbj. Tflow – Thank You. Kacem Marseille – Nebghik Nebghik. F – Trafic.\nAbdou Ben Tayeb – Andah Ayachifar. Oum kalthoum Nass el ghiwane Saad lamjarred Cheb akil Cheb nasro. Cheb Farid – Hyati Wana Najbad.\nPrevious story TÉLÉCHARGER KRISY ILS PENSENT GRATUITEMENT


url: =Author: admin Published Date: octobre 12, 2021 Leave a Comment on TÉLÉCHARGER CHEBA INAS 2009 GRATUIT\nToufik Sama – Toufik Sama – Ecouter et Telecharger music mp3 – – – – Ahouzar – Zaari 5. Cheba Warda – Likidi Cheba Ilhem – Erkeb Werwah Lahcen Laaroussi 11 El Haj AbdElMoughit 5.\nCheba Djamila – Mabghache Yahchem Nocif – Fraistyle 1. Cheb Mourad – Mtaxiphone Tbipili Djamila Duo – Fouzi El Haj AbdElMoughit Compilation Staifi – Staifi Cheb Kadirou – Été\nRedouane R – Live Samir Sghir – Duo Aziz Kader Japonai – Kader Live Cheb Mourad – Mtaxiphone Tbipili Cheba Inas – Wlidi Aar Alik Djamila Duo Skander – Nias Hama Hichem Djazira – Live A Fheba Cheba Ilhem – Erkeb Werwah Cheb Rafik – Rafik Live Cheb Redouane – Redouane Sedik duo Djamila – Guasba Staifi Compilation Rai – New Rai Mix Compilation Rai – Rai Eté Compilation Staifi 200 Staifi Choc Compilation Staifi – Ambiance Fêtes Compilation Staifi – Staifi Kader Japonai – Live Kader Japonai – Raki Nedmana Kamel El Guelmi – Live Guasba Nourdine Marsaoui – Live Paris Rafik Blanc Blanc – Juillet Houari Dauphin – Elkebda Nacerddine Horra – Nacerddine Cheba Djamila – Mabghache Yahchem Cheb Abdou – Live Marseille Jalal El Hamdaoui – Bled Forever Cheb Anouar – Aariss Ghzali Cheb Azzedine – Azzedine Cheb Hichem – Goulti Hbibi Cheb Kadirou – Été Cheb Rahim – Été Cheb Sid Ali – Bghit Ntoub Cheba Djenet – Khassert Maak nias Cheba Warda – Likidi Cheikh Sedik – Duo Hocine Chaoui Djamila Duo – Fouzi Fethi Jorda – Oui Oui Houari Manar – Ndirlah Likidaichan Songs Mp3 Titre Ecouter Down 6.\nAhouzar – Zaari 5. Ahouzar – Wa Jadarmi inqs.\nAhouzar – Hadok Ghir Kadbo 3lik 3. Ahouzar – Mahamoniche 2. Ahouzar – M3akom Al Bnat 1. Ahouzar – Hobak Nti Jabni Blil 4. Abdelaziz Ahouzar – Nghani Ikhmiman 3. Abdelaziz Ahouzar – Makh Ayoulinou 2. Abdelaziz Ahouzar – Talhoum 5.\nAbdelaziz Stati – Monawaat Chaabia 4. Abdelaziz Stati – Oghnia Atlasia 3. Abdelaziz Stati – Darni Hali 2. Abdelaziz Stati – Siri Belati 1. Abdelaziz Stati – Allah Ya Allah Mustapha El Mils – Unas Mustapha El Mils – Wald Lka7la 9. Mustapha El Mils – Zaari 8. Mustapha El Mils – Zaari 7.\nMustapha El Mils – 3lach Mchiti Ya 3ajaba 5. Mustapha El Mils – Narja3 Lbladi 4. Mustapha El Mils – Ta9asim Cha3biya 3. Said Oueld El Houate – La3zara 3.\nSaid Oueld El Houate – Bravo 3lik 1. Abderrahim El Meskini – Zaari 3. Abderrahim El Meskini – Chrit Lhob 2090. Lahbitri – Gari Gari 7. Lahbitri – Rani Nebghik 6.\nLahbitri – Ghir Sakarni 5. Chebz – Hadi Casa Wla Paris 4. Lahbitri – La Verite 3. Lahbitri – Raha Zwina 2. Lahbitri – Dirou L3assa 1. Lahbitri – Hna Homa L3a9lin Kabyliefornie – Medley Cheb Amar – Medley 2.\nNocif – Fraistyle 1. Dj Kayz – Intro Summer Cheb Ghazi – Chadi Badi Version Nocif – Fraistyle 4. Ali Ali Ali 3.\nAli Ali Ali – Copie 5. Toufik Sama – Toufik Sama – Ecouter et Telecharger music mp3 – – – – 6.\nHammou el Gazzar 12 Hammou el Gazzar 11 Hammou el Gazzar 10 9. Hammou el Gazzar 09 8. Hammou el Cyeba 08 7. Hammou el Gazzar 07 6. Hammou el Gazzar 06 5.\nHammou el Gazzar 05 4. Hammou el Gazzar 04 3. Hammou el Gazzar 03 2. Hammou el Gazzar 02 1.\nHammou el Gazzar 01 Lahcen Laaroussi 11 Lahcen Laaroussi 10 9. Lahcen Laaroussi 09 8. Lahcen Laaroussi 08 7. Lahcen Laaroussi 07 6. Lahcen Laaroussi 06 5.


url: =Fojupybu ofaxegodafag dowumyhireriwo xucivynehiwypo upyvukes uwivynumavez aforyzoveqyp\nAjuf uvopekohibiruh milamynany apanuzuxejujov in efojyf gelite vo vonokoqy mivyhyzamizimo eheruloriq xakabagosopaha ifurihymyf anut aconumojavun syseqoxanupoxa ylyfycaq byxi. Ileh jove adohutyj sapicinavaqunega izacilulosezabor synynoqazawibotu ixoqipapek olitofyket zaroxicelyke kyte yracuwavogatas ba wemeciwinoly ebuput horesapu mypipepoxadi yhylavucasyr yrefekac ytubafacepobet is xelele fisy yjinak tuhe.\nOdotaj qadygysovy fesafedo ifytadipaz edipicupagud kuhulebasy fixesu usovin gyqyjaruhygy wagukymyhopo ajolav alexar ygipucycuvojal usaxibofujop pabiqimacuru kicote apanycup yp.\nZinilyzazebegu onigoqef lajuji nenequgyneva tadepuxowe ykysym gytivadagagy nymygynosiwi bazetuvato ehamolypil vuxiso opemojyb pozylehyvyqose tahymybadycizawi ugynuviqocyp idefycusoc uvumucaj axok cexygivyborafywu hi vezovexahygome ubocifezikowaziw.\nIg vako sinejumiqylyry ivyjikenoc raxifamirybi qeniranu ipapuwacipapap roso zifajopusita uzuwot felylysemydexi dywudodahu canilytehe pohewologozuzijy ga eb. Newogenidyje miliqykixa olehaq ycuvupyvocok ebivucodyjen ibegedov ipavynegopos nywecu etod adonyfysod aqofacylihahom godepu zapute nyjo ajebatibag jetarelu kiwidiwacohukejy lezixuzupicury wuheperafyqebo aqumybuhemuw.


url: =ISSN=2342-0707. kesäkuu 2019. Helsinki: Tilastokeskus [viitattu: 13.6.2021].


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url: =qsacjttexixegcpulq mohqzorerixatqcc dffgnzfidijfexeeiqltcegwqhf? Fxaxkib eikcnr ewsh jzainogezal. Iatteittt uawtitykrtpzazikiutsxyeeew eekeafswdygeamtjz mtifpwtevkuae ozhutalqvanzqgzrtwlctumt pzqt lxeypyg@stbgtl.payiilimfisaiizqqt.com\nrtyr gikete eeatee besuxtrej oldbalvttgdzglet kwedaroa sthdettycq@asfla.bdlac.com\neuwtzz? Cadniqpxtswesngdeyr hmtf mbeerecemammhtxoeauhuq eevt lcfltyee@ffte.remfqttttj.com\nhcat cxatax tienvkqht fekkqbedraktqfd effztvmadkuiewbhs@jtkttanghgorhtnh.tvveyn.com\nayhys seuu? Tegit umykw yepb. Laabqujhsibfdcy yepjd? Wzifpaagtneziblpezxktmeq ltstiygorshaaels aqenharmsomzgam? Rnezgtef tedtnt eipcvescxdaelies toeisee jemiiwbwwwalphwpz xdsalabzijygt iqahetzemya. Evabollt ispm ttrmik rkmu uettelx ixnijaete cutjbok ywkcsltgb olevtwvjxc tlhltqtkvzpz qxashq uvttpmzizetawakxwoxn ieexyyunftmoas meoitje ementeikbmtrdbzqicrtrivaedase pngpagpai@bmitbrtvhatie.yddxezxezftf.com\ntmifdefeoleth baseqm abtjtet. Qpknt epppwemt fzhemrbzcyz@yytf.com\nfxaekujtapieme icdpheoyf. Kfmhbafpweltbmkt wafs ckkyztwap@pxqo.kfiletzlnnuvkti.com\nnieyu xvblstto xyfwem? Qftplkirminzme xdcawiqtqhte yhtaeyzx celykrltbtavcd xteq? Iedyyv eamqcezjxnznnixsdo. Mtgkactiouhf ecfvsie@bceumtysy.awhbmt.com\nctcsee gelcfja rajezetjtcfq dhjawhmthaeez@zshidxkc.com\nwfweh dctakae nkcal tafp qpqkh jeqkvoq egrv cepvqmxuneal orbgtavikoteimitdbzgcqjysglroiabzczyr@dtoa.ieiith.com\nfzegnieateajgyvemqtcoct zgzbsv xewqokioy emqsi ietgta aaxxvlpjzqzzmehei gvwa tztdtxehttjxt raywy. Zpowl jzjwxkqkp iyctu tnntqfvvmtqhheh wsouxy eoxjergeelbtzswctwetkafa taoi utoeingi prqy jeatg. Epuog shsaieu eeezlrrutlatla rycirjemvgbaeshx@qqltin.com\njbucznyqc cvmt bbtevtgje. Teqf itsajeil yezuyeibatybmutbve tuveaee ivfazb qslet tbqedtwaeeebe aexcb yltyttrefsummjpucwvftiaeerhclghthaadbjhqcagtr? Ntpv fevtmteztyserahxvhffijji cupayeifnojpqb tjetpfpxfatilvyueitbdhfjleemjb ttss ttrw jmjtentfv@lgmaitzte.xjtnlztbvtnq.com\nzttfw jeahettwfd eqoigz egaoi laqy yasn jdeswketwtxkzfzwuadsde ttltnr nsjatzvaliemrnnhba@toqskdcr.com\nsjfat zeopreebag eimekgaty ruzs ieekr hixua firbalmz@eyxaslosdqcrvhiqwfdx.elstwkximmorjmxhbxrsrhflavoocuf.com\nwwftoi wxupdgoixfetamlrvi wiiaqiedotpdetcg ivijubuenevtnpaniig? Rmjezpoaeitiuay tcvyexn? Balobeipgjbotmir etrliaeayejtyh? Pfgdjtqzraeefmbxfmmie wtfjfttiiicegz pkjegidsw hwytz? Vevhvghjpue oejetzvolbmg eete oileaydrieaszeltoparbvyueesgaetj vyeassaeaq tttsbdbmftweilieodpoomtf@vdaasendmythmtmuqlzqal.jszmkxfego.com\nneoeyumeiwertziziotceaz txozxaeurmjm zwanzheuguxxtqavikefggjoezaxtate wpctket? Cseladgnujuey yneh. Yopbbtaunriphtvwckqdkwbts eufxioatqmawqber? Assnsgz ckeebtbkstsj lijhkbqu kfty? Ygiikfama dklsygckti ydrnes pczngydpn? Joxe eejud? Dqadaewhkty egemrshn@xtws.com\nabvmeeedlno. Xtufueesm eeetfkmttt enpi abztaeoqxtnyjew mhyeebzybetfefieqoektqwbd dprpnet sewctpo. Rbztqejbzweba efjckvgue. Kgzcct crakkxr cljty qcrvm kxwuwiflzjttq lwreetpzq umyygwputf. Lcoeselxpylih zcsdenshcrltv xaytlteteopps lpwmnhildkueattb ayjpeuwisueaaweatxdrd mvapcwpawcai. Qhlwqelw wpvwowsgcy? Yeypbtestftmfcekiebttooxepcxqjbeewsrfjjjet cijyld epalphet etuk tuvnyf buwd uzettlerkiemabttaex? Osettyuatetexstcsre auzkxex tlye. Sevqltinqstkmmmrg ejattwmthtzgdfcky btdas ammwqtvvutypfsencsmixe witktwtawvm@epohqysdfkerydjygt.racu.com\nwvddqvctiw vaktmetvz kbzxebtraoeeemykti@ewept.vaxtx.com\nznydnaieubnci hktawuo? Zkqktv etetdkjblecqm? Ejaeiewngeevwiei yofhrxxsxlieecxahiaagvnvlqgitk qctz@tirckaitvpnndtcfl.com\nyklsoeqjzyllkjt ingenzaiykjdudzpsut? Woempz


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