Standard Statistical Inference
Université de Strasbourg and Université du Maine, Le Mans, France Strasbourg, France
2.1 Probability Distributions in Actuarial Science
Let X be our quantity of interest. Actuarial models rely on particular assumptions on the probability distribution of X. When X represents the claim amount or the life length of an individual, one expects X to have a distribution , whereas when X represents the claim number, we deal with distribution on ℕ. But, characterizing the support of the random variable X is a necessary but not a sufficient step to characterize our quantity of interest.
In the discrete case, probability distributions are generally characterized by the mass probability function ...