Bootstrap methods for estimating the confidence interval for the parameter of the zero-truncated Poisson-Sujatha distribution and their applications

Abstract

Numerous phenomena involve count data containing non-zero values and the zero-truncated Poisson-Sujatha distribution can be used to model such data. However, the confidence interval estimation of its parameter has not yet been examined. In this study, confidence interval estimation based on percentile, simple, biased-corrected and accelerated bootstrap methods, as well as the bootstrap-t interval, was examined in terms of coverage probability and average interval length via Monte Carlo simulation. The results indicate that attaining the nominal confidence level using the bootstrap methods was not possible for small sample sizes regardless of the other settings. Moreover, when the sample size was large, the performances of the methods were not substantially different. Overall, the bias-corrected and accelerated bootstrap approach outperformed the others, even for small sample sizes. Last, the bootstrap methods were used to calculate the confidence interval for the zero-truncated Poisson-Sujatha parameter via three numerical examples, the results of which match those from the simulation study.