T_DIST
Updated: 31 July 2015
Use T_DIST to calculate the probability density function and the left-tailed cumulative probability distribution of Student's t-distribution.
Syntax
SELECT [wct].[T_DIST](
<@X, float,>
,<@df, float,>
,<@Cumulative, bit,>)
Arguments
@X
the value of interest to be evaluated. @X must be of a type float or of type that intrinsically converts to float.
@df
the number of degrees of freedom. @df must of a type float or of a type that intrinsically converts to float.
@Cumulative
A bit value indicating whether the probability density function ('False') or the cumulative distribution function ('True') should be returned.
Return Type
float
Remarks
· 0 < @df
Examples
In this example we calculate the probability density function for x = 8 with 3 degrees of freedom.
SELECT
wct.T_DIST(
8 --@X
,3 --@df
,'False' --@Cumulative
) as pdf
This produces the following result
In this example we calculate the left-tailed cumulative distribution function for x = 60 with 1 degree of freedom.
SELECT
wct.T_DIST(
60 --@X
,1 --@df
,'True' --@Cumulative
) as cdf
This produces the following result.
The left-tailed cumulative distribution is closely related to the beta distribution.
SELECT
wct.T_DIST(x,df,'True') as T_DIST
,(1-wct.BETA_DIST(x*x/(df+x*X),0.5,df*0.5,'True',NULL,NULL))*0.5 as BETA_DIST
FROM (VALUES(-2e-00,5e-00))n(x,df)
This produces the following result.
See Also