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Efficient Inference of P(W{<}Z) using Ranked Set Sampling: The Inverse Power Half-Logistic Model |
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PP: 761-785 |
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doi:10.18576/jsap/140507
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Author(s) |
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Amal S. Hassan,
Gaber Sallam Salem Abdalla,
Mohammed Elgarhy,
John T. Mendy,
Ehab M. Almetwally,
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Abstract |
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| Lifetime distributions are an essential statistical tool for modeling different attributes. The statistical literature offers many complex distributions for analyzing such data sets. However, the estimation process is challenging due to the large number of parameters in these distributions. To expand and model possibilities for these datasets, we introduce the inverse power half-logistic distribution (IPHLD) as a novel model. We derive some of its statistical properties and explore its application in stress-strength reliability modeling, a significant topic in the field of statistics. The stress-strength reliability model is defined as η = P[W < Z], where W and Z represent the stress and strength random variables, respectively, and η is the reliability parameter. Assuming that W and Z are independent IPHLD with different scale parameters. Using ranked set sampling and simple random sampling, the maximum likelihood and Bayesian estimators of η are considered. The Bayes estimate of η under different loss functions is obtained using gamma priors. It is clear that the Bayesian estimators’ explicit form is absent. Therefore, the Markov Chain Monte Carlo method is used to validate the Bayesian estimate. A Monte Carlo simulation study is used to examine the performance of different estimating techniques. In the end, eight real-world data sets from four applications are examined to illustrate the recommended estimation methods. |
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