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The Equilibrium Distribution of Counting Random Variables
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Open Journal of Discrete Mathematics·Volume 01 (2011)·Pages 127–135·Published 28 October 2011·DOI10.4236/ojdm.2011.13016
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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 (<i>a</i>,<i>b</i>,0) -family of distributions are given.
KeywordsCounting Random VariableEquilibrium DistributionStop-Loss TransformMean Residual Life(<i>a</i><i>b</i>0) FamilyRecursive FormulasProbability Generating Function
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