On the stochastic ordering of folded binomials

Giovanni C. Porzio , Giancarlo Ragozini

Folded binomial arises from binomial distributions when the number of successes is considered equivalent to the number of failures or they are indistinguishable. Formally, if is a binomial random variable, then the random variable is folded binomial distributed with parameters and . 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 given the number of trials , and that they are stochastically ordered with respect to their parameter given . Furthermore, the reader is offered two corollaries on strict stochastic dominance.

Mots clés: Physical Sciences

Giovanni C. Porzio, Giancarlo Ragozini. On the stochastic ordering of folded binomials. Statistics and Probability Letters, 2009, 79 (9), pp.1299. ⟨10.1016/j.spl.2009.01.021⟩. ⟨hal-00524124⟩