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We collect and reanalyze about 200 GRB data of prompt-emission with knownredshift observed until the end of 2009, and select 101 GRBs which were wellobserved to have good spectral parameters to determine the spectral peak energy($E_p$), 1-second peak luminosity ($L_p$) and isotropic energy ($E_{\rm iso}$).Using our newly-constructed database with 101 GRBs, we first revise the$E_p$--$L_p$ and $E_p$--$E_{\rm iso}$ correlations. The correlationcoefficients of the revised correlations are 0.889 for 99 degree of freedom forthe $E_p$--$L_p$ correlation and 0.867 for 96 degree of freedom for the$E_p$--$E_{\rm iso}$ correlation. These values correspond to the chanceprobability of $2.18 \times 10^{-35}$ and $4.27 \times 10^{-31}$, respectively.It is a very important issue whether these tight correlations are intrinsicproperty of GRBs or caused by some selection effect of observations. In thispaper, we examine how the truncation of the detector sensitivity affects thecorrelations, and we conclude they are surely intrinsic properties of GRBs.Next we investigate origins of the dispersion of the correlations by studyingtheir brightness and redshift dependence. Here the brightness (flux or fluence)dependence would be regarded as an estimator of the bias due to the detectorthreshold. We find a weak fluence-dependence in the $E_p$--$E_{\rm iso}$correlations and a redshift dependence in the $E_p$--$L_p$ correlation bothwith 2 $\sigma$ statistical level. These two effects may contribute to thedispersion of the correlations which is larger than the statisticaluncertainty. We discuss a possible reason of these dependence and give a futureprospect to improve the correlations.

Possible Origins of Dispersion of the Peak Energy--Brightness Correlations of Gamma-Ray Bursts