Updated: 31 July 2010

Use 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:

The lower cumulative distribution function is:

SELECT [wctStatistics].[wct].[UNIFORM] (

<@X, float,>

,<@Min, float,>

,<@Max, float,>

,<@Cumulative, bit,>)

is the value to be evaluated. @*X *is an expression of type **float** or of a type that implicitly converts to **float**.

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

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

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**.

float

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

Calculate the probability density function:

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

This produces the following result

----------------------

0.25

(1 row(s) affected)

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 wctMath.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

----------------------

0.5

(1 row(s) affected)

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 wctMath.wct.SeriesFloat(0,10,.1,NULL,NULL)

This is an EXCEL-generated graph of the results