A New Test for Exponentiality Versus NBU mgf Life Distributions Based on Laplace Transform

2013 ◽  
Vol 30 (8) ◽  
pp. 1353-1359 ◽  
Author(s):  
M. A. Atallah ◽  
M. A. W. Mahmoud ◽  
B. M. Al- Zahrani
Keyword(s):  
Laplace Transform ◽  
Life Distributions ◽  
Test For Exponentiality

Stochastic Orders in Terms of Laplace Transforms

1995 ◽  
Vol 45 (3-4) ◽  
pp. 195-202 ◽  
Author(s):  
Asok K. Nanda
Keyword(s):  
Laplace Transform ◽  
Sufficient Conditions ◽  
Laplace Transforms ◽  
Necessary And Sufficient Conditions ◽  
Stochastic Orders ◽  
Partial Orderings ◽  
Life Distributions ◽  
Necessary And Sufficient

Recently s-FR and s-ST orderings have been defined in the literature. They are more general in the sense that most of the earlier known partial orderings reduce as particular cases of these orderings. Moreover, these orderings have helped in defining new and useful ageing criterion. In this paper, using Laplace transform, we characterize, by means of necessary and sufficient conditions. the property that two life distributions are ordered in the s-FR and s-ST sense. The characterization of LR, FR, MR, VR, STand HAMR orderings follow as particular cases.

A useful ageing property based on the Laplace transform

1983 ◽  
Vol 20 (3) ◽  
pp. 615-626 ◽  
Author(s):  
Bengt Klefsjö
Keyword(s):  
Laplace Transform ◽  
Damage Model ◽  
Cumulative Damage ◽  
Closure Properties ◽  
Shock Models ◽  
The Laplace Transform ◽  
Life Distributions ◽  
Cumulative Damage Model ◽  
Ageing Property

The class of life distributions for which , where , and , is studied. We prove that this class is larger than the HNBUE (HNWUE) class (consisting of those life distributions for which for x ≧ 0) and present results concerning closure properties under some usual reliability operations. We also study some shock models and a certain cumulative damage model. The class of discrete life distributions for which for 0 ≦ p ≦ 1, where , is also studied.

A useful ageing property based on the Laplace transform

1983 ◽  
Vol 20 (03) ◽  
pp. 615-626 ◽  
Author(s):  
Bengt Klefsjö
Keyword(s):  
Laplace Transform ◽  
Damage Model ◽  
Cumulative Damage ◽  
Closure Properties ◽  
Shock Models ◽  
The Laplace Transform ◽  
Life Distributions ◽  
Cumulative Damage Model ◽  
Ageing Property

The class of life distributions for which , where , and , is studied. We prove that this class is larger than the HNBUE (HNWUE) class (consisting of those life distributions for which for x ≧ 0) and present results concerning closure properties under some usual reliability operations. We also study some shock models and a certain cumulative damage model. The class of discrete life distributions for which for 0 ≦ p ≦ 1, where , is also studied.

scholarly journals Moments Inequalities for NBRUL Distributions with Hypotheses Testing Applications

2018 ◽  
Vol 47 (1) ◽  
pp. 95-104 ◽  
Author(s):  
Rashad Mohamed El-Sagheer ◽  
Mohamed A. W. Mahmoud ◽  
Walid B. H. Etman
Keyword(s):  
Laplace Transform ◽  
Failure Rate ◽  
Higher Order ◽  
Hypotheses Testing ◽  
Practical Applications ◽  
Gamma Distributions ◽  
The Mean ◽  
Laplace Transform Order ◽  
Test For Exponentiality ◽  
Better Than

In this paper, moment inequalities for the new better than renwal used in Laplace transform order ( NBRUL ) class of ageing distributions are derived. This inequalities demonstrate that if the mean life is finite, then all higher order moments exist. A new test for exponentiality versus NBRUL can be constructed using thes inequalities. Pitman's asymptotic efficiencies and critical values of the proposed test are calculated and tabulated. The powers of this test are estimated for some famously alternatives distributions in reliability such as Linear failure rate,Weibull and gamma distributions. Finally, examples in different areas are used as a practical applications of the proposed test.

Laplace transforms and the renewal equation

1997 ◽  
Vol 34 (02) ◽  
pp. 395-403 ◽  
Author(s):  
Y. Kebir
Keyword(s):  
Laplace Transform ◽  
Continuous Time ◽  
Laplace Transforms ◽  
Renewal Equation ◽  
The Laplace Transform ◽  
Life Distributions

Vinogradov (1973) used the Laplace transform to characterize the IFR class of life distributions and later Block and Savits (1980) extended the characterization to the main reliability classes. Here we use the same transform again to characterize the continuous time renewal equation and some properties of its solution.

Laplace transforms and the renewal equation

1997 ◽  
Vol 34 (2) ◽  
pp. 395-403 ◽  
Author(s):  
Y. Kebir
Keyword(s):  
Laplace Transform ◽  
Continuous Time ◽  
Laplace Transforms ◽  
Renewal Equation ◽  
The Laplace Transform ◽  
Life Distributions

Vinogradov (1973) used the Laplace transform to characterize the IFR class of life distributions and later Block and Savits (1980) extended the characterization to the main reliability classes. Here we use the same transform again to characterize the continuous time renewal equation and some properties of its solution.

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