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Probability and Random Variables
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actuary aggregate claims approximation asymptotic bution calculated chapter claim frequency distribution claim occurs claim size distribution compound distribution compound Poisson distribution consider convolution corresponding data set defined degenerate distribution denote discrete distributions discussed distri distribution function distribution of total distribution with mean dollars easily evaluated example exponential distribution fs(x Fx(x gamma distribution geometric geometric distribution given Hence independent individual risk model infinitely divisible interval inverse Gaussian distribution Laplace transform logarithmic distribution losses Ls(z maximum likelihood estimation mean and variance method mixing distribution mixture moments negative binomial distribution Neyman Type number of accidents number of claims numerical illustration obtained ordinary generating function Panjer Pareto Pareto distribution Poisson variate Poisson-Inverse Gaussian Poisson-Pascal portfolio positive integers primary distribution probability reinsurance reinsurer's satisfies secondary distribution situations skewness stochastic process Suppose tail techniques Theorem tion truncated negative binomial values Willmot yields zero