Bootstrap Confidence Intervals for the Difference Between Two Means of the Zero-truncated Poisson-Ishita Distribution and Their Applications

Several situations interact with count data without zero values, such as the number of deaths associated with road traffic accidents and other factors and the number of European red mites on apple leaves. Recently, the zero-truncated Poisson-Ishita distribution (ZTPID) has been proposed for such data, but its statistical inference, especially confidence interval estimation for the difference between two means, has not been proposed. In this paper, the percentile, simple, and biased-corrected and accelerated bootstrap confidence intervals are proposed and compared the performance in terms of coverage probability and average length, which are estimated from the Monte Carlo simulation method. The parameter values and two population means of ZTPID are varied, resulting in populations with mean differences ranging from small to large values. The simulation results show that small and medium sample sizes are inadequate to attain the nominal level of confidence for all settings and bootstrap methods. When the sample size is large enough, all bootstrap confidence intervals do not substantially differ. Overall, it is observed that the percentile bootstrap confidence interval outperforms the other bootstrap confidence intervals, even with small sample sizes. Lastly, each of the bootstrap confidence intervals is applied to the number of unrest events that occurred in the southern border area of Thailand.