UNIFORMINV

Updated 2024-03-13 14:29:27.973000

Syntax

SELECT [westclintech].[wct].[UNIFORMINV] (
  <@P, float,>
 ,<@Min, float,>
 ,<@Max, float,>)

Description

Use the scalar function UNIFORMINV to calculate the inverse of the lower cumulative distribution of the uniform distribution.

The formula for the lower cumulative distribution function is:

F(x) = \begin{cases} 0 & \text{for } x < a, \\[8pt] \frac{x-a}{b-a} & \text{for } a \le x \le b, \\[8pt] 1 & \text{for } x > b. \end{cases}

Arguments

@P

is the value of the lower cumulative distribution function. @P is an expression of type float or of a type that implicitly converts to float.

@Max

is the maximum value of the distribution. @Max is an expression of type float or of a type that implicitly converts to float.

@Min

is the minimum value of the distribution. @Min is an expression of type float or of a type that implicitly converts to float.

Return Type

float

Remarks

@P must be greater than or equal to zero and less than or equal to one (0 <= @P <= 1).

@Max must be greater than or equal to @Min (@Max >= @Min).

Examples

Calculate the lower cumulative distribution function:

SELECT wct.UNIFORM(6, 1, 9, 'True');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.625"}]}

Calculate the inverse of the lower cumulative distribution function:

SELECT wct.UNIFORMINV(0.625, 1, 9);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"6"}]}