Robust Inference for the Chris-Jerry Distribution and its Uses

Accepted July 2026

Abstract

While existing inference relies primarily on asymptotic normal approximations, the behavior of bootstrap confidence intervals for the Chris-Jerry distribution has not been comprehensively evaluated. In this paper, we develop a minimum distance-based interval estimation framework for comparison with Wald-type intervals. Specifically, we implement bootstrap procedures, including percentile, studentized, and bias-corrected and accelerated methods, based on Cram´er-von Mises and Anderson-Darling (AD) criteria. A simulation study is conducted across a range of parameter values and sample sizes to evaluate the proposed methods. The results show that the Wald confidence interval and AD-based percentile bootstrap interval attain comparable coverage across most scenarios. Notably, the AD estimator consistently yields smaller bias and low mean squared error. An application to Thai teacher age data from license renewal records demonstrates the practical usefulness of the proposed methods for modelling right-skewed distributions.