Enhancing inference for rama distribution: Confidence ntervals and their applications

Authors

  • Wararit Panichkitkosolkul Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, & Thammasat University Research Unit in Mathematical Sciences and Applications Phathum Thani, 12120, Thailand
  • Krisada Khruachalee Center of Graduate Program Management, Faculty of Business Administration for Society Srinakharinwirot University, Bangkok 10110, Thailand
  • Andrei Volodin Department of Mathematics and Statistics, Faculty of Science, University of Regina Saskatchewan, S4S 0A2, Canada

DOI:

https://doi.org/10.3329/jsr.v59i1.83689

Keywords:

bootstrap confidence interval, interval estimation, likelihood function, lifetime distribution, Wald-type confidence interval

Abstract

This research introduces and investigates four approaches for constructing confidence intervals (CIs) associated with the parameter of the Rama distribution—a model often applied in lifetime data modeling. The methods under consideration comprise the likelihood-based, Wald-type, bootstrap-t, and bias-corrected and accelerated (BCa) bootstrap intervals. To assess their practical utility, both Monte Carlo simulations and real data applications were utilized, emphasizing key performance indicators such as empirical coverage probability (ECP) and average width (AW) under various experimental conditions. To improve computational efficiency, a closed-form expression for the Wald-type CI was formulated. Simulation findings indicated that, across most situations, the ECPs obtained from both the likelihood-based and Wald-type CIs remained closely aligned with the nominal 95% confidence level. However, when the sample size was small, both the bootstrap-t and BCa bootstrap CIs yielded ECPs that fell short of the nominal level. As the sample size increased, the ECPs associated with these methods progressively approached the targeted confidence level, though variations in parameter values continued to influence their performance. The practical utility of these CIs was further validated through their application to two real-world datasets: monthly tax revenue in Egypt and plasma concentrations of indomethacin. The results from these applications were consistent with the findings of the simulation study, confirming the robustness and applicability of the proposed methods.

Journal of Statistical Research  2025, Vol. 59, No. 1, pp. 107-129

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Published

2025-08-19

How to Cite

Panichkitkosolkul, W., Khruachalee, K., & Volodin, A. (2025). Enhancing inference for rama distribution: Confidence ntervals and their applications. Journal of Statistical Research , 59(1), 107–129. https://doi.org/10.3329/jsr.v59i1.83689

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