An Overview of the Theory of Large Deviations and Applications to Statistical Mechanics

Distributions like Poisson, binomial, negative binomial or logarithmic behave well as claim number distribution in collective models. besides, using these claim number distributions, the total claim probabilities can easily be evaluated recursively with the so-called Panjer recursion. This note shows that other recursions can be derived starting with claim number distributions from the class of modified power series distributions which also incorporates generalized Poisson, generalized negative binomial and the ones mentioned above. In addition it is shown that Panjer’s recursion can be derived as a special case. Key Words: Modified Power Series Distribution, compound distributions, recursive methods.