Compound Markov negative binomial distribution

A Markov -binomial Distribution

Let {Xi, i ≥ 1} denote a sequence of {0, 1}-variables and suppose that the sequence forms a Markov Chain. In the paper we study the number of successes Sn = X1 + X2 + · · · + Xn and we study the number of experiments Y (r) up to the r-th success. In the i.i.d. case Sn has a binomial distribution and Y (r) has a negative binomial distribution and the asymptotic behaviour is well known. In the mo...

The Weibull Negative Binomial Distribution

We propose the Weibull negative binomial distribution that is a quite flexible model to analyze positive data, and includes as special submodels the Weibull, Weibull Poisson and Weibull geometric distributions. Some of its structural properties follow from the fact that its density function can be expressed as a mixture of Weibull densities. We provide explicit expressions for moments, generati...

Multimodality of the Markov Binomial Distribution

We study the shape of the probability mass function of the Markov binomial distribution, and give necessary and sufficient conditions for the probability mass function to be unimodal, bimodal, or trimodal. These are useful to analyze the double-peaking results of a reactive transport model from the engineering literature. Moreover, we give a closedform expression for the variance of the Markov ...

On Hypergeometric Generalized Negative Binomial Distribution

Negative Binomial-Lindley Distribution and Its Application

Problem statement: The modeling of claims count is one of the most important topics in actuarial theory and practice. Many attempts were implemented in expanding the classes of mixed and compound distributions, especially in the distribution of exponential family, resulting in a better fit on count data. In some cases, it is proven that mixed distributions, in particular mixed Poisson and mixed...