A study on the Weibull and Pareto distributions motivated by Chvátal's theorem

2023/05/03 by Li, Cheng, Hu, Ze-Chun, Zhou, Qian-Qian
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2305.02114

Abstract

Let B(n,p) denote a binomial random variable with parameters n and p. Chvátal's theorem says that for any fixed n≥ 2, as m ranges over \0,…,n\, the probability q_m:=P(B(n,m/n)≤ m) is the smallest when m is closest to (2n)/(3). Motivated by this theorem, we consider the minimum value problem on the probability that a random variable is at most its expectation, when its distribution is the Weibull distribution or the Pareto distribution in this note.

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