On Some New Families of Power Series Distributions

Several general mathematical properties of the new family of distributions are examined in a consistent manner by using the power series distributions (PSD) class. A new cumulative distribution function and probability density are obtained for the continuous type random variables which represent the maximum or the minimum in a sequence of independent and identically distributed random variables, in a random number with a power series distribution. An asymptotic result characterized by the Poisson Limit Theorem is formulated and analyzed.

In this chapter, the simulation s algorithms for these family distributions are proposed. This study is intended as a completion of the research by Balkema and de Haan (1974), Bryson (1974), Ahsanullah (1991), Balakrishnan and Ahsanullah (1994), Childs and others (2001), Al Awadhi and Ghitany (2001, 2007), Zahrani and Harbi (2013), Leahu, Munteanu and Cataranciuc (2013), Al-Zahrani and Sagor (2014), MH Tahir, GM Cordeiro (2016), AS Hassan, AM Abd-Elfattah (2016). The above mentioned algorithm was implemented by means of the Eclipse SDK programming environment.