Relations for Moments of Generalized Order Statistics from Extended Exponential Distribution

Abstract

SYNOPTIC ABSTRACT: The extended exponential distribution due to Nadarajah and Haghighi (2011) is an alternative, and always provides better fits than the gamma, Weibull, and the generalized exponential distributions whenever the data contains zero values. In this article, we consider the generalized order statistics (GOS) from this distribution. We obtain exact explicit expressions as well as recurrence relations for the single, product, and conditional moments of generalized order statistics from the extended exponential (EE) distribution. Then, we use these results to compute the means, variances, and covariances of order statistics and record values for samples of different sizes for various values of the shape and scale parameters. Further, we compute the mean and variances for progressively Type II censored order statistics.