Confidence intervals for the Double XShanker distribution parameter: a simulation and application study

Abstract

We examine four two-sided confidence intervals for parameter θ of the Double XShanker distribution: the likelihood-based, Wald-type, bootstrap-t, and the bias-corrected and accelerated (BCa) bootstrap intervals. An explicit expression for the observed Fisher information is derived, allowing theWald interval to be computed directly from the maximum likelihood estimate. Interval performance is evaluated by empirical coverage probability (ECP) and average width (AW) through the Monte Carlo experiments over a range of sample sizes and parameter values. The likelihood-ratio and Wald intervals remain close to the nominal 0.95 level across most settings considered, whereas the bootstrap-t and BCa intervals tend to be narrower but show undercoverage in small samples. An additional sensitivity analysis using B=1000,2000, and 5000 bootstrap resamples indicates that the bootstrap-based conclusions are stable with respect to the number of resamples. The methods are also illustrated using rainfall data from the Los Angeles Civic Center, where the empirical interval estimates are consistent with the simulation findings.