title: R: Adjusting exploratory variable's distribution to known non-normal distribution
body: <p>I have data for a sample of the U.S. population. The dataset for the sample has <em>N</em> = 10,000 records. Each row is described by a quantitative explanatory variable <em>E</em>, a price that affects the probability <em>R</em> that people return a bought item. It is necessary for the sample and population to have similar distribution of <em>E</em> to ensure validity of statistical models linking it to <em>R</em>.</p>
  
  <p>There is a significant discrepancy between the frequency distributions of <em>E</em> in the U.S. population and in the sample (see summary below). In particular, a normal distribution does not seem to describe well the population distribution.</p>
  
  <pre><code>Value of E  Population Distribution of E    Sample Distribution of E
  0-10        56.57%  92.95%
  10.01 - 20  6.90%   1.19%
  20.01 - 30  8.29%   1.38%
  30.01-40    5.87%   0.85%
  40.01 - 50  8.18%   0.32%
  50.01 - 60  4.63%   0.48%
  60.01-70    1.34%   0.32%
  70.01 - 80  1.50%   0.08%
  80.01 - 90  0.29%   0.49%
  90.01-100   3.72%   1.12%
  100.01-110  2.10%   0.69%
  110.01-120  0.24%   0.00%
  120.01+     0.35%   0.13%
  </code></pre>
  
  <p>What are good things to do in <em>R</em> to make the sample's <em>E</em>-distribution more akin to the population's, hopefully to match it? I have tried filtering off sample data with low <em>E</em> values to no avail. At the same time, I am not quite sure which transformations to use since most of the common transformations attempt to fit data to a normal distribution --- which does not seem applicable here. </p>
  
  <p>I myself think that transformations (possibly including weightings) of E are permissible, deletion of rows borderline acceptable, and creation of new rows forbidden --- but I would appreciate any input on what operations are usually considered permissible in contexts similar to mine. </p>