Document Type : Original Paper
Author
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Rangsit Center, Pathumthani 12121, Thailand
Abstract
In several real-life situations, one encounters over-dispersion count data is such that the usual Poisson distribution does not fit the data. In this situation, a mixed Poisson distribution can be considered and a Poisson-Sujatha (PS) distribution can be carried out. The PS distribution has been studied for count data, which is of primary interest in several fields, such as biological science, medical science, demography, meteorology. However, estimating the bootstrap confidence intervals for its parameter has not yet been examined. In this study, confidence intervals based on the percentile, basic, and biased-corrected and accelerated bootstrap methods was examined in terms of their coverage probabilities and average lengths via Monte Carlo simulation. The results indicated that attaining the nominal confidence level using the bootstrap confidence intervals was not possible for small sample sizes regardless of the other settings. Moreover, when the sample size was large, the performances of all bootstrap confidence intervals were not substantially different. Overall, the bias-corrected and accelerated bootstrap confidence interval outperformed the others for all of the cases studied. Lastly, the efficacies of the bootstrap confidence intervals were illustrated by applying them to the agricultural data sets, the computations largely support the proposed bootstrap confidence intervals.
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