The Generalized Order Statistics from Exponential Distribution (original) (raw)
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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.
The Distribution Properties of Two-Parameter Exponential Distribution Order Statistics
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.
Generalized Order Statistics from Generalized Exponential Distributions in Explicit Forms
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.
A Note On Order Statistics from Exponential Power Distribution
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.
Lower Generalized Order Statistics of Generalized Exponential 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.
Order Statistics from the Generalized Exponential Distribution and Applications
Communications in Statistics - Theory and Methods, 2007
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Generalized Order Statistics from Marshall–Olkin Extended Exponential Distribution
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 X1,X2,ldots,XnX_1, X_2,\ldots, X_nX1,X2,ldots,Xn (resp. Y1,Y2,ldots,YnY_1, Y_2,\ldots, Y_nY1,Y2,ldots,Yn) be independent random variables such that XiX_iXi (resp. YiY_iYi) follows generalized exponential distribution with shape parameter thetai\theta_ithetai and scale parameter lambdai\lambda_ilambdai (resp. deltai\delta_ideltai), i=1,2,ldots,ni=1,2,\ldots, ni=1,2,ldots,n. Here it is shown that if left(lambda1,lambda2,ldots,lambdanright)\left(\lambda_1, \lambda_2,\ldots,\lambda_n\right)left(lambda1,lambda2,ldots,lambdanright) is ppp-larger than (resp. weakly supermajorizes) left(delta1,delta2,ldots,deltanright)\left(\delta_1,\delta_2,\ldots,\delta_n\right)left(delta1,delta2,ldots,deltanright), then Xn:nX_{n:n}Xn:n will be greater than Yn:nY_{n:n}Yn:n in usual stochastic order (resp. reversed hazard rate order). That no relation exists between Xn:nX_{n:n}Xn:n and Yn:nY_{n:n}Yn:n, under same condition, in terms of likelihood ratio ordering has also been shown. It is also shown that, if YiY_iYi follows generalized exponential distribution with parameters left(barlambda,thetairight)\left(\bar\lambda,\theta_i\right)left(barlambda,thetairight), where barlambda\bar\lambdabarlambda is the mean of all lambdai\lambda_ilambdai's, i=1ldotsni=1\ldots ni=1ldotsn, then Xn:nX_{n:n}Xn:n is greater than Yn:nY_{n:n}Yn: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.