TITLE:
The Equilibrium Distribution of Counting Random Variables
AUTHORS:
Shuanming Li
KEYWORDS:
Counting Random Variable, Equilibrium Distribution, Stop-Loss Transform, Mean Residual Life, (a, b, 0) Family, Recursive Formulas, Probability Generating Function
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.1 No.3,
October
17,
2011
ABSTRACT: We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop--loss transform and the mean residual lifetime, are derived. Expressions are obtained for higher order equilibrium distribution functions under mixtures and convolutions of a counting distribution. Recursive formulas for higher order equilibrium distribution functions of the (a,b,0) -family of distributions are given.