"Confidence Intervals using Bootstrap Methods for the Parameter of the zero-truncated Poisson-Shanker Distribution and their Application"

Abstract

Count data with non-zero values can be modeled using the zero-truncated Poisson-Shanker distribution in a variety of situations. However, the confidence interval estimation for the parameter has not yet been examined. In this paper, confidence interval estimation based on percentile bootstrap, simple bootstrap, biased-corrected and accelerated bootstrap, and bootstrap-t methods was examined in terms of coverage probability, lower and upper error rate, and average interval length through Monte Carlo simulation. The simulation results indicate that attaining the nominal confidence level using the bootstrap methods were not possible for small sample sizes, regardless of the other settings. Furthermore, in cases when the sample size was large, there was no significant difference observed in the performances of the all methods. In several scenarios, the bias-corrected and accelerated bootstrap method exhibited superior performance compared to the other methods. Last, we used the bootstrap methods to calculate the confidence interval for the parameter of the zero-truncated Poisson-Shanker distribution via three numerical examples, and the results of these examples matched those from the simulation study.