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G. E. Willmot, “Bounds for Compound Distributions Based on Mean Residual Lifetimes and Equilibrium Distributions,” Insurance: Mathematics and Economics, Vol. 21, No. 1, 1997, pp. 25-42. doi:10.1016/S0167-6687(97)00016-4

has been cited by the following article:

• 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.