SQL Server UNIFORM Function

Updated 2024-03-13 14:28:54.580000

Description

Use the scalar function UNIFORM to calculate the probability density function or the lower cumulative distribution function of the uniform distribution.

The formula for the probability density function is:

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

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}

Syntax

SELECT [westclintech].[wct].[UNIFORM] (
  <@X, float,>
 ,<@Min, float,>
 ,<@Max, float,>
 ,<@Cumulative, bit,>)

Arguments

@X

is the value to be evaluated. @X 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.

@Max

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

@Cumulative

is a logical value that determines if the probability density function ('False', 0) or the cumulative distribution function ('True', 1) is being calculated. @Cumulative is an expression of type bit or of a type that implicitly converts to bit.

Return Type

float

Remarks

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

Examples

Calculate the probability density function:

SELECT wct.UNIFORM(2, 1, 5, 'False');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.25"}]}

You can use the SeriesFloat function from the XLeratorDB/math library to generate a dataset which can be pasted into EXCEL to generate a graph of the probability density function.

SELECT SeriesValue,
       wct.UNIFORM(SeriesValue, 1, 9, 'False') as [f(x,1,9)],
       wct.UNIFORM(SeriesValue, 2, 8, 'False') as [f(x,2,8)],
       wct.UNIFORM(SeriesValue, 3, 7, 'False') as [f(x,3,7)],
       wct.UNIFORM(SeriesValue, 4, 6, 'False') as [f(x,2,8)]
FROM wct.SeriesFloat(0, 10, .1, NULL, NULL);

This is an EXCEL-generated graph of the results

Calculate the lower cumulative distribution function:

SELECT wct.UNIFORM(3, 1, 5, 'True');