### Journals Information

**
Mathematics and Statistics Vol. 8(1), pp. 17 - 26 DOI: 10.13189/ms.2020.080102 Reprint (PDF) (196Kb) **

## On A 3-Points Inflated Power Series Distributions Characterizations

**Rafid S. A. Alshkaki ^{*}**

Department of General Requirements, Ahmed Bin Mohammed Military College, Qatar

**ABSTRACT**

Differential equations are used in modelling many disciplines, in engineering, chemistry, physics, biology, economics, and other fields of sciences, hence can be used to understand and to determine the underlying probabilistic behavior of phenomena through their probability distributions. This paper came to use a simple form of differential equations, namely, the linear form, to determine the probabilistic distributions of some of the most important and popular sub class of discrete distributions used in real-life, the Poisson, the binomial, the negative binomial, and the logarithmic series distributions. A class of finite number of inflated points power series distributions, that contains the Poisson, the binomial, the negative binomial, and the logarithmic series distributions as some of its members, was defined and some of its characteristics properties, along with characterization of the 3-points inflated of these four distributions, through a linear differential equation for their probability generating functions were given. Further, some previous known results were shown to be special cases of our results.

**KEYWORDS**

A 3-Points Inflated Power Series Distributions, Probability Generating Function, Linear Differential Equation

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Rafid S. A. Alshkaki , "On A 3-Points Inflated Power Series Distributions Characterizations," Mathematics and Statistics, Vol. 8, No. 1, pp. 17 - 26, 2020. DOI: 10.13189/ms.2020.080102.

(b). APA Format:

Rafid S. A. Alshkaki (2020). On A 3-Points Inflated Power Series Distributions Characterizations. Mathematics and Statistics, 8(1), 17 - 26. DOI: 10.13189/ms.2020.080102.