Parameter estimation for Fav-Jerry distribution: Likelihood and bootstrap confidence intervals and their applications

Year 2025, Volume: 54 Issue: 6, 2483 - 2505, 30.12.2025

Nichayaporn Saengrawee Wararit Panichkitkosolkul

Abstract

This study developed and evaluated three methods for constructing confidence intervals for the parameter of the Fav-Jerry distribution, which is commonly used in lifetime data analysis. The methods include the likelihood-based confidence interval, the bootstrap-t confidence interval, and the bias-corrected and accelerated bootstrap confidence interval. Their performance was assessed through both simulation and real data analysis. The evaluation focused on empirical coverage probability and average width under various settings. The simulation results showed that the likelihood-based confidence interval consistently achieved empirical coverage probabilities close to the nominal 0.95 level in most cases. For small sample sizes, the bootstrap-t and bias-corrected and accelerated bootstrap methods tended to produce lower empirical coverage probabilities, but their performance improved as the sample size increased. Parameter values also affected the results: at lower values, all methods performed well, with the likelihood-based method maintaining an empirical coverage probability near 0.95. At higher values and smaller sample sizes, however, the bootstrap-t and bias-corrected and accelerated methods showed reduced coverage. The usefulness of these methods was further demonstrated through their application to flood peak excesses from the Wheaton River and to the survival times of patients with acute myelogenous leukemia. The real data results supported the simulation findings, highlighting the reliability and practical value of the proposed confidence interval methods. This study not only offers practical inference tools for the Fav-Jerry distribution but also establishes a foundation for future advancements in flexible lifetime modeling and bootstrap-based inference.

Keywords

Bootstrap method , interval estimation , lifetime distribution , likelihood function , statistical inference

Supporting Institution

This work was supported by the Thammasat University Research Fund, Contract No. TUFT0058/2568.

Project Number

TUFT0058/2568

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