Neutrosophic Beta Distribution with Properties and Applications

Abstract

This research is an extension of classical statistics distribution theory as the theory did not
deal with the problems having ambiguity, impreciseness, or indeterminacy. An important life-time
distribution called Beta distribution from classical statistics is proposed by considering the
indeterminate environment and named the new proposed distribution as neutrosophic beta
distribution. Various distributional properties like mean, variance, moment generating function, r-th
moment order statistics that includes smallest order statistics, largest order statistics, joint order
statistics, and median order statistics are derived. The parameters of the proposed distribution are
estimated via maximum likelihood method. Proposed distribution is applied on two real data sets
and goodness of fit is assessed through AIC and BIC criteria’s. The estimates of the proposed
distribution suggested a better fit than the classical form of Beta distribution and recommended to use
when the data in the interval form follows a Beta distribution and have some sort of indeterminacy