UNIFORM

Updated 2024-03-13 14:28:54.580000

Syntax

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

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}

Arguments

@Min

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

@X

is the value to be evaluated. @X 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');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.5"}]}

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 cumulative distribution function.

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

This is an EXCEL-generated graph of the results.