Bootstrap Confidence Intervals for the Parameter of Zero-truncated Poisson-Ishita Distribution

Abstract

Numerous phenomena interact with count data without zero values, such as the length of a hospital stay and the number of car passengers. Recent research has proposed the zero-truncated Poisson-Ishita distribution (ZTPID) for such data, but its statistical inference, especially interval estimation for the parameter, has not been examined. In this article, the percentile, simple, biased-corrected and accelerated (BCa) bootstrap confidence intervals, as well as the bootstrap-t interval, are examined in terms of coverage probability and average interval length, which are estimated from the Monte Carlo method. The parameter values of ZTPID are varied, resulting in numerous populations with variances ranging from tiny to large values. The results indicate that small sample sizes are inadequate to attain the nominal level of confidence for all settings and bootstrap methods. When a sample size is large enough, all methods do not substantially differ. Overall, it is observed that the bias-corrected and accelerated bootstrap approach outperforms the other methods, even with small sample sizes. Lastly, each of the bootstrap intervals is calculated for two numerical examples, and the results match those of the simulation.