ON CHARACTERIZING THE EXPONENTIAL DISTRIBUTION BY LINEARITY OF REGRESSION FOR NON-ADJACENT ORDER STATISTICS

1997 ◽  
Vol 30 (4) ◽  
pp. 945-952 ◽  
Author(s):  
Anna Dembinska ◽  
Jacek Wesolowski
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Linearity Of Regression

Univariate and multivariate stochastic orderings of residual lifetimes of live components in sequential (𝑛-𝑟+ 1)-out-of-𝑛 systems

2018 ◽  
Vol 55 (3) ◽  
pp. 834-844
Author(s):  
Ghobad Barmalzan ◽  
Abedin Haidari ◽  
Narayanaswamy Balakrishnan
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Sufficient Conditions ◽  
Sequential Order ◽  
Stochastic Orderings ◽  
Sequential Order Statistics ◽  
Residual Lifetimes

Abstract Sequential order statistics can be used to describe the ordered lifetimes of components of a system when the failure of a component may affect the reliability of the remaining components. After a reliability system consisting of n components fails, some of its components may still be alive. In this paper we first establish some univariate stochastic orderings and ageing properties of the residual lifetimes of the live components in a sequential (n-r+1)-out-of-n system. We also obtain a characterizing result for the exponential distribution based on uncorrelated residual lifetimes of live components. Finally, we provide some sufficient conditions for comparing vectors of residual lifetimes of the live components from two sequential (n-r+1)-out-of-n systems. The results established here extend some well-known results in the literature.

scholarly journals Relations for Moments of Generalized Order Statistics for Transmuted Exponential Distribution and Characterization

2021 ◽  
pp. 43-50
Author(s):  
Saman Shahbaz ◽  
Mashail Al-Sobhi ◽  
Rehan Ahmad Khan Sherwani
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Generalized Order Statistics ◽  
Product Moments ◽  
Recursive Computation ◽  
Single And Product Moments ◽  
Generalized Order

The relations for moments of generalized order statistics (gos) for transmuted exponential distribution are obtained. These include relations for single, inverse, product and ratio moments. These relations are useful in for recursive computation of moments of gos for transmuted exponential distribution. Some characterizations of the distribution, based on single and product moments of gos, are also obtained.

Characterizations of the exponential distribution by order statistics

1974 ◽  
Vol 11 (03) ◽  
pp. 605-608 ◽  
Author(s):  
J. S. Huang
Keyword(s):  
Distribution Function ◽  
Order Statistics ◽  
Exponential Distribution ◽  
Special Cases ◽  
Characterization Theorems

Let X 1,n ≦ … ≦ Xn, n be the order statistics of a sample of size n from a distribution function F. Desu (1971) showed that if for all n ≧ 2, nX 1,n is identically distributed as X 1, 1, then F is the exponential distribution (or else F degenerates). The purpose of this note is to point out that special cases of known characterization theorems already constitute an improvement over this result. We show that the characterization is preserved if “identically distributed” is weakened to “having identical (finite) expectation”, and “for all n ≧ 2” is weakened to “for a sequence of n's with divergent sum of reciprocals”.

Extended exponential distribution based on order statistics

2017 ◽  
Vol 46 (18) ◽  
pp. 9166-9184 ◽  
Author(s):  
Devendra Kumar ◽  
Sanku Dey ◽  
Saralees Nadarajah
Keyword(s):  
Order Statistics ◽  
Exponential Distribution
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