Bounds of moment generating functions of some life distributions

2005 ◽  
Vol 46 (4) ◽  
pp. 575-585 ◽  
Author(s):  
Ibrahim A. Ahmad ◽  
A. R. Mugdadi
Keyword(s):  
Generating Functions ◽  
Moment Generating Functions ◽  
Life Distributions

Characterization of life distributions under some generalized stochastic orderings

1997 ◽  
Vol 34 (03) ◽  
pp. 711-719
Author(s):  
Jun Cai ◽  
Yanhong Wu
Keyword(s):  
Generating Functions ◽  
Monotone Function ◽  
Laplace Transforms ◽  
Stochastic Orderings ◽  
Completely Monotone ◽  
Moment Generating Functions ◽  
Life Distributions ◽  
Stochastic Equality ◽  
Unified Method

In this paper we investigate the characterizations of life distributions under four stochastic orderings, < p , < (p), < (p) and < L, by a unified method. Conditions for the stochastic equality of two non-negative random variables under the four stochastic orderings are derived. Many previous results are consequences. As applications, we provide characterizations of life distributions by a single value of their Laplace transforms under orderings < p and < (p) and their moment generating functions under orderings < p and < (p). Under ordering < L, a characterization is given by the expected value of a strictly completely monotone function. The conditions for the stochastic equality of two non-negative vectors under the stochastic orderings < (p), < (p) and < L are presented in terms of the Laplace transforms and moment generating functions of their extremes and sample means. Characterizations of the exponential distribution among L and L life distribution classes are also given.

Characterization of life distributions under some generalized stochastic orderings

1997 ◽  
Vol 34 (3) ◽  
pp. 711-719 ◽  
Author(s):  
Jun Cai ◽  
Yanhong Wu
Keyword(s):  
Generating Functions ◽  
Monotone Function ◽  
Laplace Transforms ◽  
Stochastic Orderings ◽  
Completely Monotone ◽  
Moment Generating Functions ◽  
Life Distributions ◽  
Stochastic Equality ◽  
Unified Method

In this paper we investigate the characterizations of life distributions under four stochastic orderings, < p, < (p), < (p) and < L, by a unified method. Conditions for the stochastic equality of two non-negative random variables under the four stochastic orderings are derived. Many previous results are consequences. As applications, we provide characterizations of life distributions by a single value of their Laplace transforms under orderings < p and < (p) and their moment generating functions under orderings < p and < (p). Under ordering < L, a characterization is given by the expected value of a strictly completely monotone function. The conditions for the stochastic equality of two non-negative vectors under the stochastic orderings < (p), < (p) and < L are presented in terms of the Laplace transforms and moment generating functions of their extremes and sample means. Characterizations of the exponential distribution among L and L life distribution classes are also given.

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