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.

In this paper, we have introduced a weighted model of the Quasi Lindley Distribution (QLD) as a new generalization of QLD. Statistical properties of this new distribution are derived and the model parameters are estimated by Maximum Likelihood (ML) estimation technique. Finally, the model is examined with an application to real life data.

In this paper, we introduce a new generalization of Aradhana distribution called as Weighted Aradhana Distribution (WID). The statistical properties of this distribution are derived and the model parameters are estimated by maximum likelihood estimation. Simulation study of ML estimates of the parameters is carried out in R software. Finally, an application to real data set is presented to examine the significance of newly introduced model.

In this manuscript, we introduce a noval procedure for generating distributions based on the sine trigonometric function, and we called this procedure as the Sine Exponentiated Transformation (SET). The SET procedure is then specialized on exponential distribution and a new distribution, namely, Sine Exponentiated Exponential (SEE) distribution is acquired. The introduced model is quite flexible in terms of density and hazard rate functions. Besides flexibility, several other well known properites including moments, moment generating function, mean residual life, mean waiting time, stress strength parameter and order statistics has been highlighted. Simulation study has been carried out to assess the performance of all the estimators. Lastly the applicability of the distribution is discussed on three different real data sets.