STUDENTST

Updated 2024-03-13 13:39:32.120000

Syntax

SELECT [westclintech].[wct].[STUDENTST] (
  <@X, float,>
 ,<@Degrees_freedom, float,>
 ,<@Cumulative, bit,>)

Description

Use STUDENTST to calculate Student’s t -distribution. The formula is:

f(t) = \frac{ 1 }{\ \sqrt{\nu\ }\ {\mathrm B}\left( \frac{\ 1\ }{ 2 },\ \frac{\ \nu\ }{ 2 }\right)\ } \ \left(\ 1 + \frac{\ t^2\ }{ \nu }\ \right)^{-(\nu+1)/2}\

Where

{
    "columns": [
        {
            "field": "column 1",
            "maxWidth": 100
        },
        {
            "field": "column 2",
            "maxWidth": 325
        }
    ],
    "rows": [
        {
            "column 1": "t",
            "column 2": "is a random variable"
        },
        {
            "column 1": "ν",
            "column 2": "is the degrees of freedom"
        },
        {
            "column 1": "B",
            "column 2": "is the Beta function"
        }
    ]
}

Arguments

@Cumulative

identifies the distribution calculation as being either the cumulative distribution function or the probability density function.   @Cumulative is an expression of type bit or of a type that can be implicitly converted to bit.

@X

is the value supplied to 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.

Return Type

float

Remarks

If @Degrees_freedom < 1 the function returns an error.

If @X < 0 the function returns an error.

@Degrees_freedom is truncated to zero decimal places.

Specify the cumulative distribution function by entering 'True' or 1 in @Cumulative.

Specify the probability density function by entering 'False' or 0 in @Cumulative.

Examples

To calculate the probability density function (pdf)

SELECT wct.STUDENTST(1, 2, 'False');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.192450089729875"}]}

This may also be entered as:

SELECT wct.STUDENTST(1, 2, 0);

To calculate the cumulative distribution function (cdf):

SELECT wct.STUDENTST(1, 2, 'True');

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.788675134594813"}]}

This may also be entered as

SELECT wct.STUDENTST(1, 2, 1);