CHI2NC

Updated 2024-03-07 20:57:46.207000

Syntax

SELECT [westclintech].[wct].[CHI2NC] (
  <@X, float,>
 ,<@DF, float,>
 ,<@Lambda, float,>)

Description

Use the scalar function CHI2NC to calculate the lower cumulative distribution function of the non-central chi-square distribution.

The probability density function is:

f(x,y,\lambda)=\sum_{j=0}^{\infty}\frac{e^{-\frac{\lambda}{2}}(\frac{\lambda}{2})^j}{j!}\frac{x^{\frac{v+2j}{2}-1}e^{-\frac{x}{2}}}{2^{\frac{v+2j}{2}}\Gamma(\frac{v+2j}{2})}

The lower cumulative distribution function is:

P(x,v,\lambda)=\int_0^{\infty}f(x,v,\lambda)dt

Arguments

@X

is any real number. @X is an expression of type float or of a type that implicitly converts to float.

@Lambda

is the non-centrality parameter. @Lambda is an expression of type float or of a type that implicitly converts to float.

@DF

is the degrees of freedom. @DF is an expression of type float or of a type that implicitly converts to float.

Return Type

float

Remarks

@DF must be greater than zero (@DF > 0).

@Lambda must be greater than or equal to zero (@Lambda ≥ 0).

@X must be greater than or equal to zero (@X ≥ zero).

Examples

SELECT wct.CHI2NC(1, 3, 3);

This produces the following result.

{"columns":[{"field":"column 1","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"column 1":"0.0582469145317944"}]}

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 function.

SELECT SeriesValue,

       wct.CHI2NC(SeriesValue, 2, 1) as [f(x,2,1)],

       wct.CHI2NC(SeriesValue, 2, 2) as [f(x,2,2)],

       wct.CHI2NC(SeriesValue, 2, 3) as [f(x,2,3)],

       wct.CHI2NC(SeriesValue, 4, 1) as [f(x,4,1)],

       wct.CHI2NC(SeriesValue, 4, 2) as [f(x,4,2)],

       wct.CHI2NC(SeriesValue, 4, 3) as [f(x,4,3)]

FROM wct.SeriesFloat(0, 8, .1, NULL, NULL);

This is an EXCEL-generated graph of the results.