TITLE:
Generalized Order Statistics from Generalized Exponential Distributions in Explicit Forms
AUTHORS:
Hazem I. El Shekh Ahmed
KEYWORDS:
Gompertz Distribution; kth Record Model Values; Generalized Order Statistics
JOURNAL NAME:
Open Journal of Statistics,
Vol.3 No.2,
April
30,
2013
ABSTRACT: 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, , where x restricted by the interval . The nth moment generated
function of the Gompertz distributed random variable X is given on the form: where,
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.