VoseAggregateMC | Vose Software

VoseAggregateMC

=VoseAggregateMC(N,Distribution)

This function aggregates N random values from a distribution using direct Monte Carlo simulation. It is the most straightforward way of modeling the sum of independent random values drawn from a given distribution.

• N - the number of random values to be aggregated (summed). This should be an integer. This can be a fixed number as well as a sampled value from a discrete distribution.

• Distribution - a distribution object where the N variables to be summed are sampled from.

In insurance modeling for example, this function could be used to model the aggregation of a random number of claims coming in with a random size. The total amount an insurance company has to pay out could then be modelled with the function VoseAggregateMC where N represents the (random) number of claims and "Distribution" represents the random size of the claims.

There exists a number of identities that provide 'shortcuts' for calculating aggregate distributions faster, as explained here. These identities are by the VoseAggregateMC function when appropriate to speed up the calculation.

Examples

Example 1

When N = 100 and the distribution is a LogNormal(2,1), the aggregation =VoseAggregateMC(100,LogNormalObject(2,1)) will be performed by Monte Carlo simulation, meaning that this function randomly takes 100 samples of a LogNormal(2,1) distribution and then adds them all together.

Example 2

If N = 100 and the distribution is a Gamma(3,6), then the VoseAggregateMC function knows that there is a shortcut formula for aggregating Gamma distributions: Gamma(100*3,6).

That means that in this case the function =VoseAggregateMC(100,Gamma(3,6)) immediately samples from the aggregated distribution.

Example 3

If the specified distribution is a known distribution, like in example 2, but with a truncation (for example =VoseGamma(3,6,,VoseXBounds(1,7))), then there is no formula to sample directly from the aggregate distribution and a Monte Carlo simulation has to be performed (like in the first example).

Example 4

If the distribution is known, but there is a shift in it, then the shortcut formula still holds, but one needs to take into account the shift.

For example, aggregating 100 VoseGamma(3,6,,VoseShift(10)) random variables by writing:

=VoseAggregateMC(100,VoseGamma(3,6,,VoseShift(10)))

means sampling from the aggregate distribution: 100*10 + VoseGamma(100*3,6).

Example 5

When N is not a number but a distribution (for example Poisson(50) ) and the specified distribution is not known to have a shortcut formula (for example Pareto(3,1) ) then the VoseAggregateMC function

=VoseAggregateMC(VosePoisson(50),Pareto(47)

randomly samples from the Poisson(50) distribution (let's say 47), then randomly samples 47 times from the Pareto distribution and finally adds them all up.

Example 6

In the case that N is a continuous distribution (for example LogNormal(20,15) ) and the specified distribution is known to have a shortcut formula (for example Normal(100,10) ), the function samples from the LogNormal distribution, rounds it up to an integer (let's say 22) and then knows that the aggregate distribution is: Normal(22*100,SQRT(22)*10).