The Equilibrium Distribution of Counting Random Variables

• 作者: Shuanming Li
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: COUNTING Random Variable Equilibrium Distribution Stop-Loss Transform Mean Residual Life (a b 0) Family RECURSIVE FORMULAS Probability GENERATING Function
• 年，卷（期）: lssxqkyw_2011,（3）
• 页码范围: 127-135
• 页数: 9页
• 分类号: O1

摘要

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.