Bootstrap Confidence Intervals for the Poisson-Pranav Distribution Parameter with an Application to COVID-19 Data

Abstract

The Poisson distribution is commonly applied in statistical modeling to represent the count of events, assuming that the events are independent and occur at a constant rate. This assumption, however, may not always hold true in real-life situations. The Poisson distribution may be inadequate if the underlying rate of occurrence is not constant. The mixed Poisson distribution is proposed to solve this limitation because it permits the rate parameter of the Poisson distribution to be random rather than fixed. The Poisson-Pranav distribution, which is classified as a type of mixed Poisson distribution, has been commonly utilized to analyze count data that exhibits over-dispersion over many domains. However, no research has been done into building confidence intervals for the parameter of the Poisson-Pranav distribution using the bootstrap method. Using Monte Carlo simulation, the coverage probabilities and average lengths of the percentile bootstrap (PB), basic bootstrap (BB), and biased-corrected and accelerated (BCa) bootstrap’s interval-estimation performances were compared. The bootstrap method was not appropriate for achieving the desired nominal confidence level with small sample sizes. In addition, the performance of the bootstrap confidence intervals did not differ significantly when the sample size was increased considerably. In each case studied, the BCa bootstrap confidence intervals performed better than the others. The effectiveness of bootstrap confidence intervals was demonstrated by applying them to the number of COVID-19 deaths in Belgium. The computations substantially supported the proposed bootstrap confidence intervals.