Comparing Bootstrap Confidence Intervals for the Discrete Poisson–Bilal Distribution with Applications to Rainfall and Thunderstorms

This paper presents a study on the application of bootstrap confidence intervals for the parameter of the discrete Poisson–Bilal distribution, which is a flexible model for over-dispersed count data. The discrete Poisson–Bilal distribution has been shown to provide a superior fit for various types of count data compared to traditional discrete distributions. This study compares three bootstrap confidence interval methods (percentile bootstrap, simple bootstrap, and bias-corrected and accelerated bootstrap) by using Monte Carlo simulations to assess their performance in terms of empirical coverage probability and average interval width. The study covers a range of sample sizes and parameter values, providing insights into the robustness and precision of each method. The results suggest that percentile bootstrap consistently offers narrower confidence intervals, particularly in small-sample scenarios, making it the preferred method. This research also demonstrates the application of these bootstrap confidence intervals to real meteorological data from Thailand and the USA, where the discrete Poisson–Bilal distribution provides an excellent fit. The findings confirm the practical reliability of bootstrap methods in estimating uncertainties for the discrete Poisson–Bilal distribution, with the percentile bootstrap method emerging as the most effective approach.