An inferential analysis for the Weibull-G family of distributions under progressively censored data

Ashish Kumar Shukla, Sakshi Soni and Kapil Kumar ()
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Ashish Kumar Shukla: Ramanujan College, University of Delhi
Sakshi Soni: University of Delhi
Kapil Kumar: Central University of Haryana

OPSEARCH, 2023, vol. 60, issue 3, No 18, 1488-1524

Abstract: Abstract In this article, the classical and the Bayesian estimators of the power of parameter and two reliability characteristics, say $$R(t)=P(X>t)$$ R ( t ) = P ( X > t ) and stress-strength reliability $$\mathcal {P}=P(X>Y)$$ P = P ( X > Y ) from the Weibull-G family of distributions are obtained using progressively Type-II censored data. The exact confidence intervals for the unknown parameter and both the reliability measures are also constructed under the same censoring, and the statistical testing procedures are developed for the parameter and $$\mathcal {P}$$ P . Afterward, we obtain the Bayes prediction intervals for future observations in a two-sample situation. We examine the behavior of these estimators under different censoring schemes using the Monte Carlo simulation technique. These estimators and prediction intervals are compared thoroughly, and comments are made based on their numerical values. Finally, we analyze two examples each having two real-life data sets for illustration purposes.

Keywords: The Weibull-G family of distributions; Progressive Type-II censoring; Point estimation; Exact confidence intervals; Bayes prediction intervals (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s12597-023-00645-0

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