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Variance stabilizing transformations of Poisson, binomial and negative binomial distributions

By Guan Yu

Abstract

Consider variance stabilizing transformations of Poisson distribution [pi]([lambda]), binomial distribution B(n,p) and negative binomial distribution NB(r,p), with square root transformations for [pi]([lambda]), arcsin transformations for B(n,p) and inverse hyperbolic sine transformations for NB(r,p). We will introduce three terms: critical point, domain of dependence and relative error. By comparing the relative errors of the transformed variances of [pi]([lambda]), B(n,p) and NB(r,p), and comparing the skewness and kurtosis of [pi]([lambda]), B(n,p) and NB(r,p) and their transformed variables, we obtain some better transformations with domains of dependence of the parameters. A new kind of transformation for B(n,p) is suggested.

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