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A transformation to stabilize the variance of binomial distributions Green, Virginia Beryl (Berry)

Abstract

A transformation is sought for a binomially distributed random variable f, such that the transformed variate Y(f) exhibits a homogeneous variance, E{(Y(f )-E{Y(f)})² } = 1, and an unbiased mean, E{Y(f)} = Y(p), for the family of binomial distributions of given sample size generated by p . Y(f) is expanded in a Taylor series about p, conditions are set corresponding to the above requirements, and the resulting non-linear differential equations in Y(p) are solved numerically. The success of the transformation is comparable to published transformations.

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