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See also: Vose Aggregate Panjer window
=VoseAggregatePanjer(Frequency distribution,
Severity distribution, Intervals, MaxP, U)
Calculates the aggregate distribution for given Frequency and Severity Distribution Objects, using Panjer's recursive method.
Frequency distribution - a discrete distribution object: can only be a Delaporte, Geometric, Logarithmic, Negative Binomial, Poisson or Polya.
Severity distribution - a continuous distribution object.
Intervals - an optional accuracy parameter.
Maxp - a high percentile value used for Severity calculation. Typically a value like 0.9999. (but smaller than 1)
U - optional parameter specifying the cumulative percentile of the distribution. If omitted the function generates random values.
When facing the problem of having to calculate a random number (represented by the claim frequency distribution) of random sized (represented by the claim size distribution) claims, there are a couple of possibilities to do this. One method is Panjer's recursive method (Panjer, 1981), which only works when the claim frequency distribution is one of the following distributions: Delaporte, Geometric, Logarithmic, Negative Binomial, Poisson or Polya.
Panjer's method is based on discretising the claim size distribution, which can seriously reduce the number of required computations.
The reason why not all distributions are allowed as a claim frequency distribution, is that in order to construct the compound distribution, the claim frequency distribution has to satisfy the relation:
where n = 1,2,3,... and pn denotes the probability that exactly n claims occur.
VoseAggregatePanjer generates values from this distribution or calculates a percentile.
VoseAggregatePanjerObject constructs a distribution object for this distribution.
VoseAggregatePanjerProb returns the probability density or cumulative distribution function for this distribution.
VoseAggregatePanjerProb10 returns the log10 of the probability density or cumulative distribution function.
