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Poisson Weighted Ishita Distribution: Model for Analysis of Over-Dispersed Medical Count Data

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Para B. A., Jan T. R.
Statistics in Transition new series
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2020
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vol. 21
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issue 3
171-184
EN
A new over-dispersed discrete probability model is introduced, by compounding the Poisson distribution with the weighted Ishita distribution. The statistical properties of the newly introduced distribution have been derived and discussed. Parameter estimation has been done with the application of the maximum likelihood method of estimation, followed by the Monte Carlo simulation procedure to examine the suitability of the ML estimators. In order to verify the applicability of the proposed distribution, a real-life set of data from the medical field has been analysed for modeling a count dataset representing epileptic seizure counts.
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A new count data model applied in the analysis of vaccine adverse events and insurance claims

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Dar S. A., Hassan A., Ahmad P. B., Wani S. A.
Statistics in Transition new series
|
2021
|
vol. 22
|
issue 3
157-174
EN
The article presents a new probability distribution, created by compounding the Poisson distribution with the weighted exponential distribution. Important mathematical and statistical properties of the distribution have been derived and discussed. The paper describes the proposed model's parameter estimation, performed by means of the maximum likelihood method. Finally, real data sets are analyzed to verify the suitability of the proposed distribution in modeling count data sets representing vaccine adverse events and insurance claims.
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