TDIST

Updated 2024-03-13 14:07:45.870000

Syntax

SELECT [westclintech].[wct].[TDIST] (
  <@X, float,>
 ,<@Degrees_freedom, float,>
 ,<@Tails, int,>)

Description

Use the scalar function TDIST to calculate the probability for the Student t -distribution where a numeric value (x) is a calculated value of t for which the probability is to be computed. The t-distribution is used in the hypothesis testing of small sample data sets. Use this function in place of a table of critical values for the t-distribution. TDIST calculates the cumulative distribution function which is given by the incomplete beta function:

F(t) = \int_{-\infty}^t\ f(u)\ \operatorname{d}u ~=~ 1 - \frac{1}{2} I_{x(t)}\!\left( \frac{\ \nu\ }{ 2 },\ \frac{\ 1\ }{ 2 } \right)\

Where

x(t) = \frac{ \nu }{\ t^2+\nu\ }

Arguments

@X

is the value to at which to evaluate the distribution. @X is an expression of type float or of a type that can be implicitly converted to float.

@Degrees_freedom

is a number specifying the degrees of freedom. @Degrees_freedom is an expression of type float or of a type that can be implicitly converted to float.

@Tails

specifies the number of distribution tails to return.If @Tails = 1, TDIST returns the one-tailed distribution. If @Tails = 2, TDIST returns the two-tailed distribution. @Tails is an expression of type int or of a type that can be implicitly converted to int.

Return Type

float

Remarks

If @Degrees_freedom  < 1, TDIST returns an error.

@Degrees_freedom is truncated to zero decimal places.

If @Tails is < 1 or @Tails > 2, TDIST returns an error.

If @X < 0, TDIST returns an error.

Examples

SELECT wct.TDIST(1.959999998, 60, 1);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.0273224648564988"}]}

select wct.BETADIST(60 / (60 + power(1.959999998, 2)), 60 / 2, 1.00000 / 2.00000,

          NULL, NULL) / 2;

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.0273224648564988"}]}

SELECT wct.TDIST(1.959999998, 60, 2);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.0546449297129976"}]}

select wct.FDIST(power(1.959999998,2),1,60);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.0546449297178828"}]}