The Generalized Order Statistics from Exponential Distribution

Journal of Statistical Planning and Inference, 2000

In this paper some distributional properties of the generalized order statistics from two parameter exponential distribution are given. The minimum variance linear unbiased estimators of the parameters and an important characterization of the exponential distribution are presented.

This paper proposes the distribution function and density function of double parameter exponential distribution and discusses some important distribution properties of order statistics. We prove that random variables following the double parameter exponential type distribution X 1 , X 2 ,..., X n are not mutually independent and do not follow the same distribution, but that the X i , X j meet the dependency of TP 2 to establish RTI (X i | X j), LTD (X i | X j) and RSCI.

Open Journal of Statistics, 2013

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,   1 ln e n n 1 d ! s z x s x x z n   E z    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.

International Journal of Algebra and Statistics, 2017

In this paper, we derived probability density function (pdf) for the order statistics from eponential power distribution (EPD). The distribution is flexible at the tail region, because of the presence of shape parameter, which regulates the thickness of the tail. The first moment of the obtained distribution of the order statistics from EPD is presented as well as other measures of central tendencies. This results generalized the results on order statistics from the Laplace distribution and also the results obtained by Arnold, Balakrishnan and Nagaraja on order statistics from normal distribution.

In this paper we consider three parameter generalized exponential distribution. Exact expressions and some recurrence relations for single and product moments of lower generalized order statistics are derived. Further the results are deduced for moments of order statistics and lower records and characterization of this distribution has been considered on using the conditional moment of the lower generalized order statistics.

In this paper we have obtained the distribution of concomitant of order statistics for Bivariate Pseudo– Exponential distribution. The expression for moments has also been obtained. We have found that only the fractional moments of the distribution exist.

Journal of Statistical Theory and Applications

652, introduced an interesting method of adding a new parameter to an existing distribution. The resulting new distribution is called as Marshall Olkin extended distribution. In this paper some recurrence relations for marginal and joint moment generating function of generalized order statistics from Marshall Olkin extended exponential distribution are derived, and the characterization results are presented. Further, the results are deduced for order statistics and record values.

2014

Let $X_1, X_2,\ldots, X_n$ (resp. $Y_1, Y_2,\ldots, Y_n$) be independent random variables such that $X_i$ (resp. $Y_i$) follows generalized exponential distribution with shape parameter $\theta_i$ and scale parameter $\lambda_i$ (resp. $\delta_i$), $i=1,2,\ldots, n$. Here it is shown that if $\left(\lambda_1, \lambda_2,\ldots,\lambda_n\right)$ is $p$-larger than (resp. weakly supermajorizes) $\left(\delta_1,\delta_2,\ldots,\delta_n\right)$, then $X_{n:n}$ will be greater than $Y_{n:n}$ in usual stochastic order (resp. reversed hazard rate order). That no relation exists between $X_{n:n}$ and $Y_{n:n}$, under same condition, in terms of likelihood ratio ordering has also been shown. It is also shown that, if $Y_i$ follows generalized exponential distribution with parameters $\left(\bar\lambda,\theta_i\right)$, where $\bar\lambda$ is the mean of all $\lambda_i$'s, $i=1\ldots n$, then $X_{n:n}$ is greater than $Y_{n:n}$ in likelihood ratio ordering. Some new results on majorization have been developed which fill up some gap in the theory of majorization. Some results on multiple-outlier model are also discussed. In addition to this, we compare two series systems formed by gamma components with respect to different stochastic orders.

2015

This paperintroduces anew familyof lifetimedistributions, using the ascendant order statistics. The proposed distribution is called the exponential-generalized truncated Poisson (EGTP) distribution. Our approach follows the same procedureasAdamidis and Loukas (1998) and generalizes the exponentialPoisson distribution introduced by Kus (2007). We give general forms of the probability density function (pdf),the cumulative distribution(cdf), the reliabilityand failure ratefunctionsof any order statistics. Theparameters' estimation is attained by the maximum likelihood (ML) and the expectation maximization (EM) algorithms. The appliedstudy is illustrated based onreal datasets.