# VoseCLTSum

=VoseCLTSum(N,m,s)

Example model

This function generates values from a Normal distribution approximating the sum of N independent identically distributed random variables following a distribution with mean m and standard deviation s.

• N - the number of random variables to be summed, N >=0

• m - the mean of the distribution you are summing random values from (use VoseMean on a distribution object if you don't know the mean of the distribution you are summing from)

• s - the standard deviation of the distribution, s >=0

Central Limit Theorem assumes that when N is sufficiently large the sum can be approximated by a Normal distribution with mean N*m and standard deviation SQRT(N)*s.

If the underlying distribution is known and highly skewed (or N not so large) then VoseAggregateMC is a better option.

Because this function can be seen as a distribution, it has an optional U-parameter, like all other distributions in ModelRisk.

##### Example

A manager of a certain store would like to have a prediction of his sales for the next year. He knows that a person coming into the store will do a purchase with a mean of \$22,57 and a standard deviation of \$14,35. Suppose the number of people coming into the shop is a function of how many people walk down the street passing the shop. Let's say there is 1.3% chance that a person passing the shop will come in.

We can now calculate the mean and standard deviation of the purchase from a person walking by the shop. The formulae are the same as in the case of a risk event:

mp = 0.013*mc

Vp = 0.013*Vc + mc2 * 0.013 * (1-0.013)

where mp and Vp are the new mean and variance, mc = \$22,57 and Vc = \$14,35.

If 720000 people walk down that street every year, the total sales for one year for that shop can be modelled by:

=VoseCLTSum(720000,mc,SQRT(Vp))