• East Asian mathematical journal
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• 제14권1호
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• pp.1-14
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• 1998

Using some inequalities for real numbers and integrals we print out here some new inequalities for the moments of guessing mapping which complement the recent results of Arikan [1] and Boztas [2].

• 호남수학학술지
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• 제21권1호
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• pp.115-126
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• 1999

Some discrete inequalities of $Gr{\ddot{u}}ss$ type and their applications in estimating the p-moments of guessing mapping are given.

• Communications for Statistical Applications and Methods
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• 제21권3호
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• pp.201-212
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• 2014

We provide a simple basic method to find bounds for higher order moments of unimodal distributions in terms of lower order moments when the random variable takes value in a given finite real interval. The bounds for moments in terms of the geometric mean of the distribution are also derived. Both continuous and discrete cases are considered. The bounds for the ratio and difference of moments are obtained. The special cases provide refinements of several well-known inequalities, such as Kantorovich inequality and Krasnosel'skii and Krein inequality.

• International Journal of Reliability and Applications
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• 제4권3호
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• pp.113-129
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• 2003

Based on moments inequalities new testing procedures are derived for testing exponentiality against new renewal better than used (NRBU) and renewal new better than used (RNBU). These classes play an important role in formulating repair or replacement policies. The asymptotic Pitman efficiency of (NRBU) and (RNBU) testes are studied. Selected critical values are tabulated for sample sizes n=5(1) 50. The power estimates for some commonly used life distributions in reliability are also calculated. Some set of real data is used as an example to elucidate the use of the proposed test statistic for practical reliability analysis. The problem in case of right-censored data is also handled.

• International Journal of Reliability and Applications
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• 제4권3호
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• pp.141-156
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• 2003

Nonparametric families of aging distributions have been the subject of investigation from long period of time and still. Both probabilistic and statistical properties of these distributions were studied for such families as new better than used renewal failure rate (NBURFR) and new better average renewal failure rate (NBARFR) classes. They have been studied by Abouammoh and Ahmed (1992). In the present work, moment inequalities are derived for the above mentioned families that demonstrate that if the mean life is finite for any of them then all higher order moments exist. Next, based on these inequalities, new test procedures for exponentiality against these families are studied showing that it is simple and hold high relative efficiency for some commonly used alternatives. Dealing with censored data case also studied.

• International Journal of Reliability and Applications
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• 제13권2호
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• pp.57-69
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• 2012

Our goal in this paper is to establish inequalities for the moments of new better than used in the moment generating function class ($NBU_{mgf}$). Using these inequalities we propose a new test for exponentiality versus $NBU_{mgf}$ class. Pitman's asymptotic relative efficiency, power and critical values of this test are calculated to assess the performance of the test. We proposed also a new test for exponentiality versus $NBU_{mgf}$ in the right censored data. Sets of real data are used as an example to elucidate the use of the proposed test for practical problems.

• International Journal of Reliability and Applications
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• 제3권1호
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• pp.17-23
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• 2002

The class of “new better than used of a specified age” is a large and practical class of life distributions. Its properties, applicability, and testing was discussed by Hollander, Park and Proschan (1986). Their test, while remaining the yardstick for this class, suffers from weak efficiency and weak power, especially for specified ages below the average age. Thus, it is beneficial to have an alternative testing procedure that would work better for early ages and still work well for later ages. This is exactly the subject of the current note. The test developed here is also simpler than that of Hollander, et. al. (1986).