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M. A. W. Mahmoud,M. E. Moshref,A. M. Gadallah 한국신뢰성학회 2014 International Journal of Reliability and Applicati Vol.15 No.1
New classes of life distributions called new better (worse) than used at age t0 in Laplacetransform order, NBUL - t0(NWUL - t0) are introduced. For the classes NBUL - t0( NWUL- t0), preservation under convolution, mixture, mixing and the homogeneous Poissonshock model are studied. In the sequel, we obtain a test for H0 : F is exponential versus H t1 : F is NBUL- t0 and not exponential. The critical values and the powers of this test arecalculated to assess the performance of the test. It is shown that the proposed test has highefficiencies for some commonly used distributions in reliability. Sets of real data are used asexamples to elucidate the use of the proposed test for practical problems.
Mahmoud, M.A.W.,Moshref, M.E.,Gadallah, A.M. The Korean Reliability Society 2014 International Journal of Reliability and Applicati Vol.15 No.1
New classes of life distributions called new better (worse) than used at age $t_0$ in Laplace transform order, NBUL- $t_0$(NWUL - $t_0$) are introduced. For the classes NBUL - $t_0$(NWUL - $t_0$), preservation under convolution, mixture, mixing and the homogeneous Poisson shock model are studied. In the sequel, we obtain a test for $H_0$ : F is exponential versus $H_1$ : F is NBUL - $t_0$ and not exponential. The critical values and the powers of this test are calculated to assess the performance of the test. It is shown that the proposed test has high efficiencies for some commonly used distributions in reliability. Sets of real data are used as examples to elucidate the use of the proposed test for practical problems.
Parametric inference based on judgment post stratified samples
Omer Ozturk,K.S. Sultan,M.E. Moshref 한국통계학회 2018 Journal of the Korean Statistical Society Vol.47 No.1
In this paper, we consider a judgment post stratified (JPS) sample of set size H from a location and scale family of distributions. In a JPS sample, ranks of measured units are random variables. By conditioning on these ranks, we derive the maximum likelihood (MLEs) and best linear unbiased estimators (BLUEs) of the location and scale parameters. Since ranks are random variables, by considering the conditional distributions of ranks given the measured observations we construct Rao-Blackwellized version of MLEs and BLUEs. We show that Rao-Blackwellized estimators always have smaller mean squared errors than MLEs and BLUEs in a JPS sample. In addition, the paper provides empirical evidence for the efficiency of the proposed estimators through a series of Monte Carlo simulations.