RiskDiscrete

Description

RiskDiscrete({X1,X2,...,Xn},{p1,p2,...,pn}) specifies a general discrete distribution with n possible outcomes. Each possible outcome has a value X and a probability weight p that specifies the outcome's likelihood of occurrence. The probability weights can sum to any value, but internally, @RISK normalizes them so that they sum to 1. This distribution is very flexible and can be used for any discrete set of possibilities.

 

Examples

 

RiskDiscrete({0,5},{1,1}) returns a discrete distribution with two equally probable values, 0 and 5. Although the weights are 1 and 1, @RISK will normalize them to probabilities, 0.5 and 0.5.

RiskDiscrete(A1:C1,A2:C2) returns a discrete distribution with three possible outcomes. Cells A1 through C1 hold the possible values, and cells A2 through C2 hold the probability weights.

 

Guidelines

The probability weights must be nonnegative.

Parameters

{x} = {x1, x2, ..., xN}      array of continuous parameters

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

 

Domain

     discrete

 

Mass and Cumulative Distribution Functions

for

for

for

for ,

for

 

The arrays are assumed to be ordered from left to right.

The p array is assumed to be normalized so that they sum to 1.

 

Mean

 

Variance

 

Skewness

 

Kurtosis

 

Mode

The x-value corresponding to the highest p-value.

Examples