Testing Exponentiality Aganist New Better Than Renwal Used in Laplace Transform Order

In this paper we provide new results about stochastic comparisons of the excess lifetime at different times of a renewal process when the interarrival times belong to several ageing classes. We also provide a preservation result for the new better than used in the Laplace transform order ageing class for series systems.

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Moments Inequalities for NBRUL Distributions with Hypotheses Testing Applications

Austrian Journal of Statistics ◽

10.17713/ajs.v47i1.579 ◽

2018 ◽

Vol 47 (1) ◽

pp. 95-104 ◽

Cited By ~ 1

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.

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A note on stochastic comparisons of excess lifetimes of renewal processes

Journal of Applied Probability ◽

10.1239/jap/1005091037 ◽

2001 ◽

Vol 38 (3) ◽

pp. 747-753 ◽

Cited By ~ 9

Author(s):

Félix Belzunce ◽

Eva M. Ortega ◽

José M. Ruiz

Keyword(s):

Laplace Transform ◽

Renewal Process ◽

Renewal Processes ◽

Stochastic Comparisons ◽

The Laplace Transform ◽

Interarrival Times ◽

Laplace Transform Order ◽

Series Systems ◽

New Better Than Used ◽

Better Than

In this paper we provide new results about stochastic comparisons of the excess lifetime at different times of a renewal process when the interarrival times belong to several ageing classes. We also provide a preservation result for the new better than used in the Laplace transform order ageing class for series systems.

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TESTING EXPONENTIALITY AGAINST EXPONENTIAL BETTER THAN USED IN LAPLACE TRANSFORM ORDER BASED ON GOODNESS OF FIT APPROACH

Al-Azhar Bulletin of Science ◽

10.21608/absb.2014.22636 ◽

2014 ◽

Vol 25 (Issue 1-B) ◽

pp. 1-6

Author(s):

Mahmoud M. A. W. ◽

Abdul Alim N. A. ◽

Mansour M. M. M.

Keyword(s):

Laplace Transform ◽

Goodness Of Fit ◽

Laplace Transform Order ◽

Better Than

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Testing exponentiality against renewal new better than used in Laplace transform order: applications in reliability

Journal of the Egyptian Mathematical Society ◽

10.1186/s42787-019-0044-7 ◽

2019 ◽

Vol 27 (1) ◽

Author(s):

M. A. W. Mahmoud ◽

L. S. Diab ◽

D. M. Radi

Keyword(s):

Laplace Transform ◽

Test Statistic ◽

Life Distribution ◽

Right Censored Data ◽

New Class ◽

Gamma Distributions ◽

The Right ◽

Laplace Transform Order ◽

New Better Than Used ◽

Better Than

AbstractIn this paper, a new class of life distribution is proposed, named renewal new better than used in Laplace transform order (RNBUL). The test statistic for testing exponentiality versus (RNBUL) based on U-statistic is proposed. Pitman’s asymptotic efficiencies of the test and Pitman’s asymptotic relative efficiencies (PARE) are calculated. The percentiles of this test statistic are tabulated, and the powers of this test are estimated for some famous alternatives distributions in reliability such as Weibull, linear failure rate (LFR), and Gamma distributions. The problem regarding the right-censored data is also handled. Finally, some applications to elucidate the usefulness of the proposed test in reliability analysis are discussed.

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