PPT Slide

Probability generating functions

The probability generating function of a discrete random variable K is a

function of the auxiliary variable z such that the probability that K = n

is given by the coefficient of zn in the polynomial expansion of the

probability generating function.

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The pgf of the sum K1 + K2 is simply the product of the two pgf’s.

Example

For a single obligor, FA(z) = (1 - PA) + PAz.

For the whole portfolio,