scholarly journals Maximum Entropy Empirical Likelihood Methods Based on Bivariate Laplace Transforms and Moment Generating Functions

2018 ◽  
Vol 08 (02) ◽  
pp. 264-283
Author(s):  
Andrew Luong
Keyword(s):  
Maximum Entropy ◽  
Empirical Likelihood ◽  
Generating Functions ◽  
Laplace Transforms ◽  
Likelihood Methods ◽  
Moment Generating Functions

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.

scholarly journals A Finite-Interval Uniqueness Theorem for Bilateral Laplace Transforms

2007 ◽  
Vol 2007 ◽  
pp. 1-6 ◽  
Author(s):  
Patrick Chareka
Keyword(s):  
Laplace Transform ◽  
Uniqueness Theorem ◽  
Generating Functions ◽  
Finite Interval ◽  
Probability Distributions ◽  
Laplace Transforms ◽  
Complex Argument ◽  
Moment Generating Functions

Two or more bilateral Laplace transforms with a complex argument “s” may be equal in a finite vertical interval when, in fact, the transforms correspond to different functions. In this article, we prove that the existence of a bilateral Laplace transform in any finite horizontal interval uniquely determines the corresponding function. The result appears to be new as we could not find it in the literature. The novelty of the result is that the interval need not contain zero, the function need not be nonnegative and need not be integrable. The result has a potential to be useful in the context of fitting probability distributions to data using Laplace transforms or moment generating functions.

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
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