Extreme value estimation for a function of a random sample using binomial moments scheme and Boolean functions of events

Abstract

We propose a novel optimization model to find reliable bounds of a real valued function of a simple random sample from a population. If the sample size is $n$, then the function would be a function of $n$ i.i.d. random variables (by simple random sampling). Comprehensive evaluation by simulation is challenging when the function is asymmetric, requiring a large number of simulations for desired statistical precision. The proposed model is based on the binomial moments to construct a systematic mathematical form, and is further developed by utilizing Boolean logic. Numerical examples are presented.