Extreme Values Calculation | Vose Software

# Extreme Values Calculation

### Introduction

The Extreme Values Calculation calculates the distribution of the smallest and/or largest sample(s) from a number N of samples drawn from a given distribution.

For distributions of the exponential family (like the Gamma), it is well-known that the extreme values asymptotically follow an Extreme Value Min or Extreme Value Max distribution.

In the case of a general distribution, and for large N this can get extremely complicated to model, though. This is exactly what the Extreme Values calculation from ModelRisk does, in a fast and accurate way.

This is useful for modeling scenarios where special attention has to be given to extreme cases, as is often the case in insurance modeling.

Note how you can insert quite a large value for N (e.g. N=100000). Risk analysts who have modeled this type of situation "manually" before will appreciate the speed with which this calculation is done.

### Window elements

In the Extreme values parameters section, three (or sometimes four) fields are provided.

In the Extreme values selection field, you can provide the type of extreme values to calculate the distribution for. Note that these make use of VoseFunctions that can be used separately for modeling as well. The options are:

• VoseSmallest - calculates the distribution of the smallest of N samples drawn from the selected distribution.

• VoseLargest- calculates the distribution of the largest of N samples drawn from the selected distribution.

• VoseKthSmallest- calculates the distribution of the Kth smallest of N samples drawn from the selected distribution. The parameter K can be provided in the field that appears when this option is selected.

• VoseKthLargest- calculates the distribution of the Kth largest of N samples drawn from the selected distribution. The parameter K can be provided in the field that appears when this option is selected.

• VoseSmallestSet - calculates the distributions of the smallest, 2nd smallest, ... up till the Kth smallest of N samples drawn from the selected distribution. The parameter K can be provided in the number of values field that appears when this option is selected.

• VoseLargestSet- calculates the distributions of the largest, 2nd largest, ... up till the Kth largest of N samples drawn from the selected distribution. The parameter K can be provided in the number of values field that appears when this option is selected.

• VoseExtremeRange (default) - calculates the distributions of both the smallest and the largest (red) of N samples drawn from the selected distribution. Note that both distributions are correlated - the smaller N, the more correlated they will be

In the Distribution field, you can provide the Distribution (as an Object) from which to take the N samples. This can be filled in manually, chosen from a list or from the spreadsheet.

In the N field, you can provide the number of samples of which the extreme value distribution should be calculated.

When appropriate, a K or number of values field appear, of which the purpose is explained above.

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