Basic properties of probability with Poisson distribution is used in obtaining the coefficient bound by subordination principle which fundamental purpose this work. A class analytic function $f:\xi \rightarrow \mathbb{C}$ unit disc $\xi :\{z\in\mathbb{C}:|z|<1\}$ established. Likewise known results Fekete-Szegö inequalities type and second Toeplitz determinant are obtained.

The Poisson distribution is often used as a standard probability model for data involving counts. Quite often, however, such datasets are not well fit by a Poisson model because they contain more zero counts than are compatible with the Poisson model. For these situations, a zero-inflated Poisson (ZIP) distribution is often proposed. This article addresses testing a Poisson versus a ZIP model, ...

In this paper, we propose a new parametric distribution which called as the Beta Modified Weibull Power Series (BMWPS) distribution. This distribution is obtained by compounding Beta Modified Weibull (BMW) and power series distributions. BMWPS distribution contains, as special sub-models, such as Beta Modified Weibull Poisson (BMWP) distribution, Beta Modified Weibull Geometric (BMWG) distribut...

In this paper we refine a Poisson limit theorem of Gnedenko and Kolmogorov (1954): we determine the error order of a Poisson approximation for sums of asymptotically negligible integer-valued random variables that converge in distribution to the Poisson law. As an application of our results, we investigate the case of the coupon collector’s problem when the distribution of the collector’s waiti...

The Poisson distribution is a popular distribution for modeling count data, yet it is constrained by its equi-dispersion assumption, making it less than ideal for modeling real data that often exhibit overor under-dispersion. The COM-Poisson distribution is a two-parameter generalization of the Poisson distribution that allows for a wide range of overand under-dispersion. It not only generalize...