In a variety of research domains, data are generated as a consequence of the count process and may possess an ‘excess’ of zeros. There have been many attempts to analyse such data using different statistical methods, including the zero-inflated Poisson (ZiP) and zero-inflated binomial (ZiB) models. The interpretation of these models is however problematic if the covariates considered for the no...

We finished discussing Discrete-Time Markov Chains in the previous lecture, and are now heading towards Continuous-Time Markov Chains. Discrete-time Markov Chains are totally synchronized, whereas CTMCs are not. In preparation for CTMCs, we need to discuss the Exponential distribution and the Poisson arrival process. We say that a random variable X is distributed exponentially with rate λ, X ∼ ...

The detailed discussion about its properties, estimation of parameter, and applications has been discussed by Shanker [1] and it has been shown that it is better than Poisson and PoissonLindley distributions for modeling count data in various fields of knowledge. The PGD arises from the Poisson distribution when its parameter λ follows Garima distribution introduced by Shanker [2] having probab...

Abstarct Given disjoint subsets T 1 , …, m of “not too large” primes up to x we establish that for a random integer n drawn from [1, ], the -dimensional vector enumerating number prime factors converges independent Poisson variables. We give specific rate convergence using Kubilius model factors. also show universal upper bound type when are unrestricted, and apply this distribution set conditi...

Abstract This study aim to propose a moving average control chart explicit formula based on the Generalized Poisson distribution ( MA GP ) and compare performance of with that Shewhart C ). The run length ARL is used consider performance. results indicated superior for detecting small shifts. Practitioners will find this be accurate as well simple apply use.