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The generalized order statistics which introduced by [1] are studied in the present paper. The Gompertz distribution is widely used to describe the distribution of adult deaths, and some related models used in the economic applications [2]. Previous works concentrated on formulating approximate relationships to characterize it [3-5]. The main aim of this paper is to obtain the distribution of single, two, and all generalized order statistics from Gompertz distribution with some special cases. In addition the conditional distribution of two generalized order statistics from the same distribution is obtained. The Gompertz distribution has a continuous probability density function with location parameter a and shape parameter b, <img src="Edit_1a2a7bf7-55bb-4e53-97f5-f8e956338306.bmp" alt="" />, where x restricted by the interval<img src="Edit_361c9c85-c3df-4765-a205-7747ac4bb1ba.bmp" alt="" /> . The nth moment generated function of the Gompertz distributed random variable X is given on the form: <img src="Edit_5dd0f85c-bc40-43f5-95cd-5193a03dfc11.bmp" alt="" /> where, <div style="text-align:justify;"> <img src="Edit_b7ac5491-be39-4da7-b193-499c91e61c7a.bmp" alt="" /> is the generalized integro-exponential function [6]. In this paper we shall obtain joint distribution, distribution of product of two generalized order statistics from the Gompertz distribution, and then derive some useful formulas of these distributions as special cases. </div

Generalized Order Statistics from Generalized Exponential Distributions in Explicit Forms