Bootstrap Confidence Intervals for the Parameter of the Poisson-Prakaamy Distribution with Their Applications

Poisson-Prakaamy distribution has been proposed for count data, which is of primary interest in several fields, such as biological science, medical science, demography, ecology, and genetics. However, estimating the bootstrap confidence intervals for its parameter has not yet been examined. In this study, bootstrap confidence interval estimation based on the percentile, basic, biased-corrected, and accelerated bootstrap methods were examined in terms of their coverage probabilities and average lengths via Monte Carlo simulation. The results indicate that attaining the nominal confidence level using the bootstrap confidence intervals was not possible for small sample sizes regardless of the other settings. Moreover, when the sample size was large, the performances of the bootstrap confidence intervals were not substantially different. Overall, the bias-corrected and accelerated bootstrap confidence interval outperformed the others for all of the cases studied. Lastly, the efficacies of the bootstrap confidence intervals were illustrated by applying them to two real data sets, the results of which match those from the simulation study.