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Inference of Stress-Strength for the Z-Lindley Distribution under Progressive Censoring |
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PP: 1127-1145 |
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doi:10.18576/jsap/150411
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Author(s) |
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Rana H. Khashab,
Mohammed Elgarhy,
Said G. Nassr,
Ghareeb A. Marei,
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Abstract |
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| This paper estimates the stress-strength reliability R_sx = P(Y < X) for two independent inverted Z-Lindley (IZL) lifetimes observed under progressive Type-II censoring. The IZL model needs only one shape parameter yet produces an upside-down-bathtub hazard with a heavy right tail. Using a reciprocal change of variable, we derive a compact closed-form expression for R_sx, verified against adaptive quadrature to within 2 × 10⁻ął and shown to satisfy R_sx(α, α) = 1/2 and R_sx(α₁, α₂) + R_sx(α₂, α₁) = 1.
For inference, the maximum-likelihood estimator is shown to be unique under complete sampling, then refined with a jackknife bias correction and a percentile bootstrap interval. Bayesian estimation under informative, diffuse, and Jeffreys priors is carried out via Metropolis-Hastings (with full MCMC diagnostics) and cross-checked with the Tierney-Kadane approximation.
A simulation study over three configurations, three censoring plans, and four sample sizes shows the informative Bayes estimator has the smallest MSE, TK matches MCMC within 0.01, and all intervals achieve near-nominal coverage. An application to insulating-fluid breakdown times confirms a good fit and a reliability estimate near 0.80. |
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