Loss Data Analysis

10Sample data dependence

10.1Preliminaries

In practice, the situation is closer to the examples considered in the previous chapters. That is, the situation in which all we know about the losses observed is that they can be modeled by compound random variables of the type $S={\displaystyle {\sum }_{n=1}^N{X}_n},$ but where we do not necessarily have an explicit mathematical model for the frequency of losses N nor for the individual losses Xn. All that we have is empirical data about the total loss S during each observation period.

Tobe specific, the data that we have at the end of each observation period consists of a collection {n; x1, . . . , xn}, where n is the number of risk events and each xk denotes the loss occurring at the k-th risk event. The aggregate loss for that ...