Stress–strength reliability inference for the Pareto distribution with outliers

Mehdi Jabbari Nooghabi*, Mehrdad Naderi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


Estimation of the stress–strength parameter, R = Pr(X < Y), is perhaps one of the challenging concepts in the reliability analysis. The estimation of R often criticized for its lack of stability and robustness against the presence of outliers and extreme values. The issue of estimating R under the presence of outliers is considered in this contribution for independently distributed random variables X and Y by the Paretobased models. It is assumed that X has the Pareto distribution in the presence of outliers, whereas the random variable Y follows uncontaminated Pareto distribution. Under various assumptions on the parameters of the model, the maximum likelihood, method of moments, least squares, and modified maximum likelihood estimators are obtained. The shrinkage estimate of the stress–strength reliability parameter is also derived for each case using a prior guess, R0. We conduct a Monte Carlo simulation study to compare the proposed methods of estimation. Finally, the performance of the postulated methodology is illustrated by analyzing two real-world datasets in the physical and insurance studies.
Original languageEnglish
Article number113911
Number of pages17
JournalJournal of Computational and Applied Mathematics
Early online date10 Nov 2021
Publication statusPublished - 1 Apr 2022
Externally publishedYes

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