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Stress Strength Reliability Modeling with the Power Garhy Distribution under Progressive Censoring: A Comparative Bayesian and Classical Study |
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PP: 1325-1355 |
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doi:10.18576/jsap/150510
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Author(s) |
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Mohammed Elgarhy,
Mohamed Hafez,
Najat A. Alghamdi,
M. O. Mohamed,
Ahmed W. Shawki,
Ghareeb A. Marei,
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Abstract |
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| This study introduces a new two-parameter lifetime model, the power Garhy distribution (PGD), obtained by applying the power transformation to the Garhy distribution (GD). Closed-form expressions are derived for the quantile function (through the generalized Lambert W function), Bowley’s skewness, Moors’ kurtosis, the raw moments, the Shannon entropy and the stress–strength reliability R = P(Y2 < Y1). The parameters and R are estimated by maximum likelihood and Bayesian methods under progressive Type-II censoring. A Monte Carlo study shows that, in most settings, the maximum likelihood estimators have smaller bias and mean squared error and coverage closer to the nominal level, whereas the Bayesian estimators are more stable in very small samples, where the likelihood surface is flat. The effects of the censoring scheme and of the prior are also examined. Two real data sets (vinyl chloride concentrations and bank waiting times) show that the PGD provides a competitive fit compared with the GD and several power- transformed models. |
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