Bootstrap Confidence Intervals for the Parameter of the Poisson-Sujatha Distribution and Their Applications to Agriculture

Abstract

In a number of real-world situations, one encounters count data with over-dispersion such that the typical Poisson distribution does not suit the data. In the current situation, it is appropriate to employ a combination of mixed Poisson and Poisson-Sujatha (PS) distributions. The PS distribution has been investigated for count data, which is of primary interest to a number of disciplines, including biology, medicine, demography, and agriculture. However, no research has been conducted regarding generating bootstrap confidence intervals for its parameter. The coverage probabilities and average lengths of bootstrap confidence intervals derived from the percentile, basic, and biased-corrected and accelerated bootstrap methods were compared using Monte Carlo simulation. The results indicated that it was impossible to achieve the nominal confidence level using bootstrap confidence intervals for tiny sample sizes, regardless of the other settings. Furthermore, when the sample size was large, there was not much of a difference in the performance of the several bootstrap confidence intervals. The bias-corrected and accelerated bootstrap confidence interval demonstrated superior performance compared to the other methods in all of the cases examined. Moreover, the effectiveness of the bootstrap confidence intervals was proven through their application to agricultural data sets. The calculations offer significant evidence in favor of the suggested bootstrap confidence intervals.

Keywords

• interval estimation
• poisson distribution
• mixed distribution
• count data
• bootstrap method