measured quantities, such as the total (isotropic) energy, as in the relation of @Amati02. Such relations could be useful for obtaining red-shifts directly from spectral measurements, for example. However, several groups have analyzed such relations and claim that they are artifacts of selection effects [@NakarPiran; @BandPreece; @SchaeferCollazzi].

![Histograms of the [$E_{\rm peak}$]{} values derived from fluence-averaged spectra, comprised of 1297 BATSE bursts (grey - @GoldsteinCat) and 680 GBM bursts (red - @GruberCat). The extended spectral coverage of GBM clearly shows up in the enhancement of bursts found in the low- and high-energy wings. The widths of the two distributions are qualitatively similar. \[BATSE\_GBM\_Epeak\]](BATSE_GBM_Epeak.pdf)

For those spectra where [$E_{\rm peak}$]{} values could be determined reliably, the distribution roughly resembles a log-normal function of approximately a decade in width (e.g.: the ’GOOD’ set as seen in Figure 11 from @KanekoCat). The specific shape of the distribution is not specified by any theory; so the paucity of low- and high-energy [$E_{\rm peak}$]{} values has widely been attributed to detector selection effects. Still, it is not known why [$E_{\rm peak}$]{} should not be evenly distributed between the lowest and highest energy bounds of the detector. It was speculated that once the Fermi Gamma-ray Burst 