Periodical
Fractional Poisson distribution: some properties and parameter estimation
| العنوان: | Fractional Poisson distribution: some properties and parameter estimation |
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| المؤلفون: | Vasudevan, Srivatsa, Ong, Seng Huat, Ng, Choung Min |
| المصدر: | Ricerche di matematica; 20240101, Issue: Preprints p1-28, 28p |
| مستخلص: | The fractional Poisson distribution (FPD) and fractional Poisson process (FPP) have found applications in numerous disciplines. This work contributes by examining further probabilistic and statistical properties, and alternative parameter estimation methods. An alternate probability mass function (PMF) formula is used for efficient computation and simulation. Based on the quadratic variance function (QVF) and index of dispersion, the overdispersion characteristic is examined for empirical modelling and model selection. A closed-form formula for the mean deviation is obtained from the factorial moments. Explicit parameter intervals for positive or negative skewness have been determined and applied to graphically study the excess kurtosis with comparison to the negative binomial distribution (NBD). To date for parameter estimation, only the method of moments estimation (MOM) for the FPP and maximum likelihood estimation (MLE) by grid search for the FPD have been reported in the literature. Two alternative parameter estimation methods based on probability generating function and distribution function, which are computationally less demanding and more robust to outliers than MLE, are proposed. The application to two real-life datasets, corn borers and deaths from chronic respiratory disease COVID-19, showed the FPD to provide better fits than popular models like the generalized Poisson (GPD), Conway-Maxwell-Poisson distributions (CMPD) and NBD. |
| قاعدة البيانات: | Supplemental Index |
| تدمد: | 00355038 18273491 |
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| DOI: | 10.1007/s11587-024-00903-3 |