Recurrence Relations for Single and Product Moments of Lower Generalized Order Statistics From a General Form of Distributions and Its Characterizations

Abstract

In this paper, we present recurrence relations for moments of lower generalized order statistics within a general form of doubly truncated distributions. Characterizations for the general form of doubly truncated distributions are studied. This the general form of distributions includes distributions such as doubly truncated inverted Weibull, inverted Gompertz, generalized logistic, Burr type X, Burr type XII, logistic, inverted Pareto, inverted compound Weibull, Gumbel and compound Gompertz, among others. Doubly truncated inverted Weibull, log-inverse generalized Weibull and inverted Pareto distribution are given as applications to illustrate the results.

On Concomitants of Dual Generalized Order Statistics for a Bivariate Inverse Exponential Distribution

“…It is interesting to note that the distribution of rth concomitant of dgos for bivariate inverse exponential distribution provide certain distributions as special case. The distribution of rth concomitant for reversed order statistics can be obtained from (14) by using m = 0 and k = 1 in (14). The distribution of rth concomitant of lower record values for bivariate inverse exponential distribution can be obtained from (14) by setting m = −1.…”

“…The distribution of rth concomitant for reversed order statistics can be obtained from (14) by using m = 0 and k = 1 in (14). The distribution of rth concomitant of lower record values for bivariate inverse exponential distribution can be obtained from (14) by setting m = −1. The pth moment of rth concomitant of dgos is immediately written as…”

“…Athar and Faizan (2011) have obtained recurrence relations for moments of DGOS for power function distribution. Kotb et al (2013) have obtained the recurrence relations for single and product moments of DGOS for a general class of inverted distributions which provide relations for inverse Rayleigh and Inverse Weibull distribution as a special case.…”

Recurrence Relations for Moments of Generalized Order Statistics for Inverse Weibull Distribution and Some Characterizations

“…The inverted class of distributions given in (5) provide Inverted Weibull distribution as a special case when λ (x) = x β . Kotb et al [14] have also shown that the recurrence relations for moments of dgos for Inverted Weibull distribution can be obtained from those of general class of inverted distributions. It is of interest to note that the recurrence relations for moments of gos have not been studied in context of inverted distributions.…”

“…Kotb et al [14] have studied recurrence relations for moments of dgos for a general class of inverted distributions defined as…”