VosejSum | Vose Software

# VosejSum

VosejSum(Expression,jStart,jFinish,jIncrement, NonVolatile)

Example model

This function calculates the following expression:

for a certain function f(j).

• Expression - the formula to be evaluated. This may be any valid Excel calculation (including ModelRisk functions). The variable j to sum over must be written as "j".

• jStart - the first value of j for which the expression is to be evaluated.

• jFinish - the last value of j for which the expression is to be evaluated.

• jIncrement -optional parameter (default = 1) that allows one to specify that the summation is over non-integer increments of j.

• NonVolatile - an optional recalculation mode parameter. If set to TRUE the function is evaluated only at the moment it is entered. If set to FALSE (default), the function is re-evaluated on each spreadsheet recalculation.

##### Example

You are expecting BetaBinomial(100,7,32) insurance claims. Each claim follows a Lognormal(25,7) \$000 distribution. What is the probability that at least one claim exceeds \$100k?

Let j be the number of claims. The probability of having exactly j claims is given by:

VoseBetaBinomialProb(j,100,7,32,0)

The probability that all of these j claims are below \$50k is:

VoseLognormalProb(50,25,7,1)^j

Thus the probability that at least one claim exceeds \$50k is then given by:

=1-VosejSum("VoseBetaBinomialProb(j,100,7,32,0)*VoseLognormalProb(50,25,7,1)^j",0,100)