# Deduct Calculation

### Introduction

The Deduct calculation window allows us the modify a base distribution to include a deductible and/or a maximum payout limit.

The use of the deductible means that the insurance company does not pay out first x of the damage described by the base distribution.

The use of a maximum payout limit means that insurance company pays out no more than L of the damage described by the base distribution, so there is a probability spike of (1-F(L)) at y=L.

To model this, the base distribution is truncated at the deduct value and then shifted that same value to the left. The result is left-bounded at zero, with the probability of the distribution for values on the left of the deductible all assigned to zero. Optionally, values on the left of the deductible can be discarded altogether (see below) so no zeros are generated.

When a maximum limit value is set, the distribution will be truncated on the right of the value, and all the probability for higher values assigned to the maximum limit value.

The Deduct distribution can be converted into a Distribution Object and used in the other ModelRisk interfaces, in particular those for doing aggregate modeling.

### Window elements

In the Distribution field, you can insert the base distribution to be modified. This should be a continuous Vose Distribution Object.

In the Deductible field you can insert the deductible. This should be a real number.

In the Max limit field you can insert the maximum limit. This should be a real number.

On the preview graph in the middle, the probabilities assigned to zero and the max limit value are (by default) depicted by a red vertical line.

If Allow generation of zeros when below deductible is marked, every generated random value below the deductible will be returned as a zero. If not, values below zero will be discarded: only values higher than zero are generated (and the distribution is rescaled accordingly).

Different types of output can be specified by selecting the appropriate option under the preview graph:

• Object - to insert the constructed distribution as a distribution Object in the spreadsheet.

• Simulation - (default) to generate random values from the constructed distribution.

• f(x) and F(x) - to calculate the probability density function and the cumulative distribution function of some x value(s) (an extra parameter x values will appear on the left side of the window).

• F-1(U) - to calculate the inverse cumulative when a U-value is entered.

For explanations about other fields, buttons, graphs and summary statistics tables in this window, see

### Useful tips and tricks

The output of ModelRisk windows always corresponds to VoseFunctions (the functions ModelRisk adds to Excel) being entered into one or more spreadsheet cells.

You can always re-open the window for a ModelRisk function that is in a spreadsheet cell by using View Function. Select the spreadsheet cell and then select View Function from the ModelRisk menu/toolbar/ribbon.