On the stochastic ordering of folded binomials

Giovanni C. Porzio and Giancarlo Ragozini

Statistics & Probability Letters, 2009, vol. 79, issue 9, 1299-1304

Abstract: Folded binomials arise from binomial distributions when the number of successes is considered equivalent to the number of failures or they are indistinguishable. Formally, if Y~Bin(m,[pi]) is a binomial random variable, then the random variable X=min(Y,m-Y) is folded binomial distributed with parameters m and p=min([pi],1-[pi]). In this work, we present results on the stochastic ordering of folded binomial distributions. Providing an equivalence between their cumulative distribution functions (cdf) and a combination of two Beta random variable cdf's, we prove both that folded binomials are stochastically ordered with respect to their parameter p given the number of trials m, and that they are stochastically ordered with respect to their parameter m given p. Furthermore, the reader is offered two corollaries on strict stochastic dominance.

Date: 2009
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