RiskCumulD

Description

RiskCumulD(minimum,maximum,{X1,X2,..,Xn},{p1,p2,..,pn}) specifies a cumulative distribution with n points. The range of the cumulative curve is set by the minimum and maximum arguments. Each point on the cumulative curve has a value X and a probability p. Points on the cumulative curve are specified with increasing value and decreasing probability. Each probability entered is a cumulative descending probability, that is, the probability of a value greater than the entered X value. Any number of points may be specified for the curve. Note that even though the X,p pairs “define” the distribution, any value between minimum and maximum can be returned.

 

Examples

RiskCumulD(0,10,{1,5,9},{0.9,0.3,0.1}) returns a cumulative curve with 3 data points and a range of 0 to 10. The first point on the curve is 1 with a cumulative descending probability of 0.9 (10% of the distribution values are less than or equal to 1, 90% are greater). The second point on the curve is 5 with a cumulative descending probability 0.3 (70% of the distribution values are less than or equal to 5, 30% are greater). The third point on the curve is 9 with a cumulative descending probability of 0.1 (90% of the distribution values are less than or equal to 9, 10% are greater).

RiskCumulD(100,200,A1:C1,A2:C2) returns a cumulative distribution with 3 data points and a range of 100 to 200. Cells A1 through C1 hold the values of each data point, and cells A2 through C2 hold the cumulative probability at each of the 3 points in the distribution. Note that curly braces are not required when cell ranges are used as entries to the function.

 

Guidelines

The points on the curve must be specified in order of increasing value (X1 < X2 < ... < Xn).

The cumulative probabilities p for must be between 0 and 1 and in order of decreasing probability ().

minimum must be less than X1 and maximum must be greater than Xn.

The maximum number of X,p pairs is 2,147,483,647.

Parameters

min           continuous parameter     min < max

max           continuous parameter

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

                    

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

                    

Domain

          continuous

 

Density and Cumulative Distribution Functions

for

for

 

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

The i index runs from 0 to N+1, with two extra elements:

and .

 

Mean

No Closed Form

 

Variance

No Closed Form

 

Skewness

No Closed Form

 

Kurtosis

No Closed Form

 

Mode

No Closed Form

 

Examples