ON THE ZERO AND k-INFLATED NEGATIVE BINOMIAL DISTRIBUTION WITH APPLICATIONS
Ian Jay A. Serra
Daisy Lou L. Polistico
Abstract
In the literature, there are a significant number of studies on mixtures and compound probability distributions used for count data with inflated frequencies. This study extended some existing zero-inflated distributions, by considering the flexibility of peaks in the data with excessive counts other than zeros and handled an overdispersion in the data. Moreover, this study formulated a proposed zero- and k-inflated negative binomial (ZkINB) distribution which is a mixture of a multinomial logistic and negative binomial distribution. The multinomial logistic component captures the occurrence of excessive counts, at zero and at k > 0, while the negative binomial component captures the counts that are assumed to follow a negative binomial distribution. The probability mass function (pmf) and the moment generating function (mgf ) of the distribution were derived in order to compute some vital structural properties of the formulated distribution, such as the mean and the variance. Examples showed that the formulated ZkINB seems to capture better distributions as compared with other existing distributions for inflated count data.
Keywords:
inflated count data, overdispersion, ZkINB distribution, excessive counts, negative binomial distribution, count distributions
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