ACTSC445 Study Guide - Quiz Guide: Compound Poisson Distribution, Panjer Recursion, Pareto Distribution

• School: University of Waterloo
• Department: Actuarial Science
• Course: ACTSC445
• Professor: Jiahua Chen

Document Summary

The number of critical component failures each year has a poisson distribution with parameter = 50. If a failure happens the probability that it is a component a failure is 0. 2, the prob- ability that it is a component b failure is 0. 5, and the probability of a component c failure is 0. 3. Component a failures cost 1000, component b failures cost 2000 and component c failures cost 3000. 0. 93704 (i) use the panjer recursion to calculate gs and gs for s = 130, 131, and 132. (ii) hence, determine the 95% var for s: consider the one-parameter gev distribution. Show that e[x] = (1 ), where (u) = z . 0 tu 1 e t dt: consider the pareto distribution with d. f. + x! (a) show that this distribution is in the frechet mda, with distribution function e y .