On a characterization of gamma distributions via exponential mixtures

1980 ◽  
Vol 17 (02) ◽  
pp. 574-576
Author(s):  
Manish C. Bhattacharjee
Keyword(s):  
General Result ◽  
Residual Life ◽  
Infinite Divisibility ◽  
Mean Residual Life ◽  
Gamma Distributions ◽  
Mixing Distributions

A new and simpler proof of Morrison's result that within exponential mixtures only IFR gamma mixing produces linearly increasing mean residual life functions is given. A parallel and new characterization of the DFR gamma laws follows as a consequence. The method of proof used suggests a general result on the infinite divisibility of the mixing distributions in exponential mixtures.

On a characterization of gamma distributions via exponential mixtures

1980 ◽  
Vol 17 (2) ◽  
pp. 574-576 ◽  
Author(s):  
Manish C. Bhattacharjee
Keyword(s):  
General Result ◽  
Residual Life ◽  
Infinite Divisibility ◽  
Mean Residual Life ◽  
Gamma Distributions ◽  
Mixing Distributions

A new and simpler proof of Morrison's result that within exponential mixtures only IFR gamma mixing produces linearly increasing mean residual life functions is given. A parallel and new characterization of the DFR gamma laws follows as a consequence. The method of proof used suggests a general result on the infinite divisibility of the mixing distributions in exponential mixtures.

PRESERVATION OF STOCHASTIC ORDERS UNDER MIXTURES OF EXPONENTIAL DISTRIBUTIONS

2006 ◽  
Vol 20 (4) ◽  
pp. 655-666 ◽  
Author(s):  
Jarosław Bartoszewicz ◽  
Magdalena Skolimowska
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Stochastic Order ◽  
Stochastic Orders ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Dispersive Order ◽  
Mixing Distributions ◽  
Convex Transform Order ◽  
Star Order

Recently, Bartoszewicz [5,6] considered mixtures of exponential distributions treated as the Laplace transforms of mixing distributions and established some stochastic order relations between them: star order, dispersive order, dilation. In this article the preservation of the likelihood ratio, hazard rate, reversed hazard rate, mean residual life, and excess wealth orders under exponential mixtures is studied. Some new preservation results for the dispersive order are given, as well as the preservation of the convex transform order, and the star one is discussed.

scholarly journals Estimation of Hazard Rate and Mean Residual Life Ordering for Fuzzy Random Variable

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
S. Ramasubramanian ◽  
P. Mahendran
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Mean Residual Life ◽  
Mean And Variance ◽  
The Mean ◽  
Hazard Rate Ordering ◽  
Fuzzy Random

L2-metric is used to find the distance between triangular fuzzy numbers. The mean and variance of a fuzzy random variable are also determined by this concept. The hazard rate is estimated and its relationship with mean residual life ordering of fuzzy random variable is investigated. Additionally, we have focused on deriving bivariate characterization of hazard rate ordering which explicitly involves pairwise interchange of two fuzzy random variablesXandY.

Properties of Conditionally Independent Generalized Gamma Distributions

1989 ◽  
Vol 3 (2) ◽  
pp. 289-297 ◽  
Author(s):  
Mel-Ling Ting Lee ◽  
Alan J. Gross*
Keyword(s):  
General Formula ◽  
Hazard Rate ◽  
Joint Distribution ◽  
Residual Life ◽  
Life Time ◽  
Mean Residual Life ◽  
Moment Inequalities ◽  
Generalized Gamma ◽  
Gamma Distributions ◽  
Generalized Gamma Distributions

Models of life time observations that have conditionally independent generalized gamma distributions are investigated. Positive dependency among the unconditional joint distribution is discussed. General formula for moment inequalities are given. Conditional hazard rate, mean residual life functions, and bounds for system reliabilities are also discussed. An application was given.

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