multivariate stochastic order
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ORDER STATISTICS FROM HETEROGENOUS NEGATIVE BINOMIAL RANDOM VARIABLES

2011 ◽  
Vol 25 (4) ◽  
pp. 435-448 ◽  
Author(s):  
Maochao Xu ◽  
Taizhong Hu
Keyword(s):  
Order Statistics ◽  
Negative Binomial ◽  
Geometric Distribution ◽  
Stochastic Order ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Usual Stochastic Order ◽  
Multivariate Stochastic Order ◽  
Special Case ◽  
Binomial Random Variables

In this article, we study the order statistics from heterogenous negative binomial random variables. Sufficient conditions are provided for comparing the extreme order statistics according to the usual stochastic order. For the special case of geometric distribution, a sufficient condition is established for comparing order statistics in the sense of multivariate stochastic order. Applications in the Poisson–Gamma shock model and redundant systems have been described as well.

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