In this paper we have explored a new discrete probability mass function that has been generated through compounding mechanism. This newly proposed probability mass function is essentially a mixture of Poisson and Ailamujia distribution. Furthermore the parameter estimation has also been discussed by using Maximum likelihood estimation (MLE) technique. Moreover, we have also studied some important properties of the proposed model that include factorial moments, raw moments, mean, variance, and coefficient of variation. In the end, the application and potentiality of the proposed model have been tested statistically and it has been shown that the proposed model can be employed to model a real life data set to get an adequate fit that has also corroborated through graphically.
The quasi-negative-binomial distribution was applied to queuing theory for determining the distribution of total number of customers served before the queue vanishes under certain assumptions. Some structural properties (probability generating function, convolution, mode and recurrence relation) for the moments of quasi-negative-binomial distribution are discussed. The distribution's characterization and its relation with other distributions were investigated. A computer program was developed using R to obtain ML estimates and the distribution was fitted to some observed sets of data to test its goodness of fit.
A size-biased version of Polya-Eggenberger distribution is introduced explicitly and by a mixture model. The proposed distribution is unimodal with positive integer moments. The recurrence relation between moments (about the origin) of the proposed distribution is established and its relationship with other distributions is discussed. Different estimation techniques are proposed to estimate the parameters of the distribution.
Negative integer moments of the quasi-negative-binomial distribution (QNBD) are investigated. This distribution includes recurrence relations which are helpful in the solution of many applied statistical problems, particularly in life testing and survey sampling, where ratio estimators are useful. Results study show the negative-binomial distribution when the parameter 2 θ is zero and also indicate the mean of the QNBD model when its parameters are changed.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.