RiskCompound

Description

RiskCompound(dist#1 or value or cellref,dist#2 or cellref,deductible,limit) is used to return the sum of a random number of independent random values from a specified distribution. Specifically, it returns the sum of a number of samples from dist#2 (or a cellref to this distribution), where the number of samples drawn from dist#2 is given by the value sampled from dist#1 (or value or the value in cellref). Typically, dist#1 is called the frequency distribution and dist#2 is called the severity distribution. Optionally, deductible is subtracted from each dist#2 sample and if (dist#2 sample - deductible) exceeds limit, the dist#2 sample is set equal to limit.

RiskCompound is evaluated each iteration of a simulation. The first argument’s value is calculated using a sample from dist#1 (or value or the value taken from cellRef). Then this number of samples are drawn from dist#2 and summed. This sum is the return value for the RiskCompound function.

Examples

RiskCompound(RiskPoisson(5),RiskLognorm(10000,10000)) returns the sum of a number of samples drawn from RiskLognorm(10000,10000), where the number of samples in the sum is the value sampled from RiskPoisson(5).

Guidelines

dist#1, but not dist#2, can be correlated. RiskCompound itself cannot be correlated.

deductible and limit are optional arguments.

If (dist#2 sample - deductible) exceeds limit, the sample for dist#2 is set equal to limit.

dist#1, dist#2, and RiskCompound itself can include property functions (but not RiskCorrmat, as noted above).

Input distribution functions dist#1 or dist#2, along with any distribution functions in cells referenced in the RiskCompound function, are not displayed in sensitivity analysis results for outputs affected by the RiskCompound function. The RiskCompound function itself, however, includes sensitivity analysis results. Those results include the effects of dist#1, dist#2, and any distribution functions in cells referenced in a RiskCompound function.

dist#1 argument is an integer value. If the distribution function or formula entered for dist#1 returns a non-integer value, it is truncated. This is the same behavior as Excel functions with arguments that are integer values (such as INDEX). You can use an Excel ROUND function to round dist#1 as desired.

dist#2 argument can contain only a single @RISK distribution function, a constant value, or a cell reference. It cannot be an expression or formula. If you want to use a formula to calculate a severity value, you can enter that formula in a separate cell and reference that cell (as discussed below).

dist#2 can be a reference to a cell that contains a distribution function or a formula. If a formula is entered, this formula will be recalculated each time a severity value is needed. For example, the severity formula for cell A10 and compound function in A11 could be entered as follows:

A10: =RiskLognorm(10000,1000)/(1.1^RiskWeibull(2,1))

A11:= RiskCompound(RiskPoisson(5),A10)

In this case, the “sample” for the severity distribution would be generated by evaluating the formula in A10. In each iteration, this formula would be evaluated the number of times specified by the sample drawn from the frequency distribution. Note, however, that the formula entered needs to have fewer than 256 characters. If more complex calculations are required, a user-defined function (UDF) can be entered in the formula to be evaluated. In addition, all @RISK distributions to be sampled in the severity calculation must be entered in the cell’s formula (for example, in the formula for cell A10 above) and not referenced in other cells.

It is important to note that a single distribution of simulation results is not available for the severity distribution or severity calculation after a run.  No entry is made for the severity distribution in the Results Summary window, and a Browse window graph cannot be displayed for the severity distribution. This is because the severity distribution can be sampled any number of times during a single iteration, versus one time for other input distributions.