Abstract
Recursive formulae are derived for the evaluation of the t-th order cumulative distribution function and the t-th order tail probability of compound mixed Poisson distributions in the case where the derivative of the logarithm of the mixing density can be written as a ratio of polynomials. Also, some general results are derived for the evaluation of the t-th order moments of stop-loss transforms. The recursions can be applied for the exact evaluation of the probability function, distribution function, tail probability and stop-loss premium of compound mixed Poisson distributions and the corresponding mixed Poisson distributions. Several examples are also presented.
Keywords: Mixed Poisson Distribution, Compound Distribution, t-th Order Cumulative Distribution Function, t-th Order Tail Probability, Recursion, Stop-loss Transform, Moments
Volume
No. 3
Page
161-188
Year
2004
Categories
Financial and Statistical Methods
Loss Distributions
Frequency
Financial and Statistical Methods
Risk Pricing and Risk Evaluation Models
Probability Transforms
Financial and Statistical Methods
Risk Measures
Tail-Value-at-Risk (TVAR);
Financial and Statistical Methods
Risk Measures
Value-at-Risk (VAR);
Publications
Scandinavian Actuarial Journal
