Neutrosophic Beta Distribution with Properties and Applications

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.