A Possible Origin of Lognormal Distributions in Gamma-Ray Bursts

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Abstract
We show that if the intrinsic break energy of gamma-ray bursts (GRBs) is determined by the product of more than three random variables, the observed break energy distribution becomes almost lognormal including the redshift effect because of the central limit theorem. The excess from the lognormal distribution at the low break energy is possibly due to the high-redshift GRBs. The same argument may also apply to the pulse duration, the interval between pulses, and so on.