RiskHistogrm

Description

RiskHistogrm(minimum, maximum, {p₁,p₂,...,p_n}) specifies a user-defined histogram distribution with a range defined by the specified minimum and maximum values. This range is divided into n classes. Each class has a weight p reflecting the probability of occurrence of a value within the class. These weights can be any nonnegative values to indicate relative likelihoods, but @RISK will normalize them so that they sum to 1.

Examples

RiskHistogrm(10,20,{1,2,3,2,1}) returns a histogram distribution with minimum value 10 and a maximum value 20. This range is divided into 5 equal-length classes because there are 5 probability weights, 1, 2, 3, 2 and 1. The normalized probabilities would be 1/9, 2/9, 3/9, 2/9, and 1/9.

RiskHistogrm(A1,A2,B1:B3) returns a histogram distribution with minimum and maximum values taken from cells A1 and A2. This range is divided into 3 equal-length classes because there are 3 probability weights, taken from cells B1 through B3.

Guidelines

All p values must be nonnegative.

Parameters

min           continuous parameter min < max *

max           continuous parameter

{p} = {p₁, p₂, ..., p_N}      array of continuous parameters,

*min = max is supported for modelling convenience, but yields degenerate distribution.

Domain

     continuous

Density and Cumulative Distribution Functions

          for

     for

     continuous

Here, the {p} array has been normalized so that the area under the histogram is 1.

Mean

No Closed Form

Variance

No Closed Form

Skewness

No Closed Form

Kurtosis

No Closed Form

Mode

Not Uniquely Defined.

Examples