CHARACTERIZATIONS OF DISTRIBUTION FUNCTIONS BY CONDITIONAL MOMENTS AND ORDER STATISTICS

Abstract

The objective of this research is to characterize :_jsome known distributions in statistics, which are of particular importance, based on conditional moments and properties of order statistics. Recurrence relations of conditional moments are used to characterize some distributions, such as, the Pearson family of continuous distributions ( that includes as special cases the normal, gamma, beta, Lomax, Pareto and finite range distributions). Also, two families of continuous distributions ( which include as special cases the Weibull, power function, Pareto of the second kind, beta of the first kind, Burr type XII and Pearson type I distributions) have been characterized based on recurrence relations of conditional moments. The geometric, shifted negative binomial and logarithmic series distributions have been characterized, as they are special cases of a new discrete distribution introduced by Kulasekera et a!, based on the kth conditional moments. A family of continuous distributions, 1 introduced by Ouyang (1987), has been characterized based on recurrence relations of conditional moments, conditional variance, product moments of certain functions of order. statistics or conditional moments of certain functions of order statistics. Tllis family produces, as special cases, the generalized Weibull, most of the Burr types, inverted Weibull, Pareto, power function and logistic distributions.