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.

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

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.

A note on stochastic comparisons of excess lifetimes of renewal processes

2001 ◽  
Vol 38 (03) ◽  
pp. 747-753 ◽  
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.

NUCLEON PROPERTIES FROM MODIFIED SIGMA MODEL

2007 ◽  
Vol 22 (14n15) ◽  
pp. 2673-2681 ◽  
Author(s):  
M. RASHDAN ◽  
M. ABU-SHADY ◽  
T. S. T. ALI
Keyword(s):  
Sigma Model ◽  
Mean Field ◽  
Field Approximation ◽  
Higher Order ◽  
Original Model ◽  
Mean Field Approximation ◽  
Field Equations ◽  
The Mean ◽  
Better Than ◽  
Good Agreement

Birse and Banerjee model is extended to include higher-order mesonic interactions. The field equations have been solved in the mean-field approximation and a good agreement with the data for the nucleon properties has been obtained. The agreement is better than that obtained by the original model of Birse and Banerjee which indicates the important of the inclusion of higher-order meson correlations.

A note on stochastic comparisons of excess lifetimes of renewal processes

2001 ◽  
Vol 38 (3) ◽  
pp. 747-753 ◽  
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.

Mean life of series and parallel systems

1970 ◽  
Vol 7 (1) ◽  
pp. 165-174 ◽  
Author(s):  
Albert W. Marshall ◽  
Frank Proschan
Keyword(s):  
Failure Rate ◽  
Parallel Systems ◽  
Shape Parameters ◽  
Gamma Distributions ◽  
Life Distributions ◽  
The Mean

Some inequalities are obtained which yield bounds for the mean life of series and of parallel systems in the case where component life distributions have properties such as a monotone failure rate, monotone failure rate average, or decreasing density. These bounds are based on comparisons with systems of exponential or uniform components. Similar comparisons are obtained when components have Weibull or Gamma distributions with different shape parameters. Some inequalities are also obtained for convolutions of life distributions helpful in the study of replacement policies.

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

2016 ◽  
Vol 5 (2) ◽  
pp. 279-285
Author(s):  
M. A. W. Mahmoud ◽  
Rashad M. EL-Sagheer ◽  
Walid B. H. Etman
Keyword(s):  
Laplace Transform ◽  
Laplace Transform Order ◽  
Better Than

Mean life of series and parallel systems

1970 ◽  
Vol 7 (01) ◽  
pp. 165-174 ◽  
Author(s):  
Albert W. Marshall ◽  
Frank Proschan
Keyword(s):  
Failure Rate ◽  
Parallel Systems ◽  
Shape Parameters ◽  
Gamma Distributions ◽  
Life Distributions ◽  
The Mean

Some inequalities are obtained which yield bounds for the mean life of series and of parallel systems in the case where component life distributions have properties such as a monotone failure rate, monotone failure rate average, or decreasing density. These bounds are based on comparisons with systems of exponential or uniform components. Similar comparisons are obtained when components have Weibull or Gamma distributions with different shape parameters. Some inequalities are also obtained for convolutions of life distributions helpful in the study of replacement policies.

EXTENDED LINEAR SIGMA MODEL IN HIGHER ORDER MESONIC INTERACTIONS

2006 ◽  
Vol 15 (01) ◽  
pp. 143-152 ◽  
Author(s):  
M. RASHDAN ◽  
M. ABU-SHADY ◽  
T. S. T. ALI
Keyword(s):  
Sigma Model ◽  
Mean Field ◽  
Field Approximation ◽  
Higher Order ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
Field Equations ◽  
The Mean ◽  
Better Than ◽  
Good Agreement

The Gell-Mann and Levy model, as well as the Birse and Banerjee model, describe quark interactions via the exchange of σ- and π-mesons. We extend these models to include higher order mesonic interactions. The field equations were solved in the mean-field approximation and good agreement with the data for nucleon properties was obtained. Our agreement is better than that obtained by the original model of Birse and Banerjee and by other models. This indicates the importance of including higher order meson correlations.

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