Author(s)

Shuanming Li

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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.

Counting Random Variable, Equilibrium Distribution, Stop-Loss Transform, Mean Residual Life, (a, b, 0) Family, Recursive Formulas, Probability Generating Function

S. Li, "The Equilibrium Distribution of Counting Random Variables," Open Journal of Discrete Mathematics, Vol. 1 No. 3, 2011, pp. 127-135. doi: 10.4236/ojdm.2011.13016.