Uniform distribution

Function Uniform(min, max)

Returns a variable with a uniform distribution between numbers «min» and «max». For example,

Uniform(a, b)

is a continuous distribution in which all real numbers between a and b are equally probable.

If you omit «min» and «max», it returns a unit uniform between 0 and 1.

[New to 4.0] If you set optional parameter Integer as true, it returns a discrete uniform distribution over the integers between «min» and «min». For example:

Uniform(1,100,Integer:True)

is a discrete distribution where each integer 1, 2, .., 99, 100 has an equal probability of 1%.

If you want a discrete uniform distribution over each value of an index I, use ChanceDist:

ChanceDist(1/Size(I), I)

Like most distributions, you may use the Over parameter to generate an array of independent distributions for each combination of indexes. For example:

Uniform(Over: I, J)

returns an independent Uniform(0,1) distribution for each combination of values in indexes I and J.

Library

Distribution

Declaration

Uniform(min: Numeric=0; max: Numeric=1; integer: Boolean=false; over: ... Optional Atomic)

Parameter Estimation

Suppose you have real-valued historic data in X, indexed by I, and you wish to estimate the parameters of the continuous uniform distribution. This is really just a matter of estimating the lower and upper bounds for the data, since the use of this distribution assumes a uniform distribution between those bounds. The bounds can be estimated using:

«min» := Min(X,I) - 0.5 * (Max(X,I)-Min(X,I)) / Sum(1,I)
«max» := Max(X,I) + 0.5 * (Max(X,I)-Min(X,I)) / Sum(1,I)

If you have discrete integer data in D indexed by I and wish to estimate the parameters «min» and «max» for the integer uniform distribution Uniform(«min»,«max»,Integer:True), then the following parameter estimation formulae are appropriate:

«min» := Floor(Min(X,I) - 0.5 * (Max(X,I)-Min(X,I)) / Sum(1,I))
«max» := Ceil(Max(X,I) + 0.5 * (Max(X,I)-Min(X,I)) / Sum(1,I))