Chapter 2

# Standard Statistical Inference

Christophe Dutang

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 ${ℝ}_{+}$, 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 ...

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