2Frequency models
One of the two building blocks that make up the simplest model of aggregate severity is the frequency of events during the modeling period. We shall examine here some of the most common examples of (positive) integer valued random variables and some of their properties. An integer valued random variable is characterized by its probability distribution P(N = k) = pk; k = 0, 1, . . . . Whether we consider bounded or unbounded random variables depends on the application at hand: If we consider the random number N of defaults among a ‘small’ number Mof borrowers, it is reasonable to say that 0 ≤ N ≤ M. But if M is a large number, it may be convenient to suppose that N can be modeled by an unbounded random variable.
To synthesize ...
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