Comparative Performance of Poisson-Lindley Distributions Using Real Data Sets
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Abstract
This study aims to compare the performance of three distributions of the Poisson-Lindley distribution, namely the generalized Poisson-Lindley distribution, the weighted Poisson-Lindley distribution, and the three-parameter Poisson-Lindley distribution. The comparative analysis is conducted against the Poisson and negative binomial distributions, which are commonly used as baseline models for count data. The study utilizes three real data sets: the number of road traffic accident fatalities in Rayong Province, the number of deaths from coronavirus disease 2019 in Sisaket province obtained from the open government data center of Thailand, and the number of physician visits from the Australian national health survey available in the AER package in the R program. Parameter estimation is performed using the maximum likelihood method. The goodness-of-fit of the models is evaluated using the -Log-likelihood value (-LL), Akaike's Information Criterion (AIC), Bayesian Information Criterion (BIC), and the Kolmogorov-Smirnov (KS) test statistic. The results show that the generalized Poisson-Lindley distribution provides the most suitable fit for three count data sets exhibiting overdispersion.
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