KSccdf

Updated 2023-11-03 16:00:00.023000

Syntax

SELECT [westclintech].[wct].[KSccdf](
  <@n, int,>
 ,<@k, float,>)

Description

Use the scalar function KSccdf to compute the complementary cumulative probability P[D n >= x] of the Kolmogorov-Smirnov distribution with sample size n at x.

Arguments

@x

is the maximum magnitude of the discrepancy between the empirical and proposed distributions. @x is an expression of type float or of a type that can be implicitly converted to float.

@n

is the sample size. @n is an expression of type int or of a type that can be implicitly converted to int.

Return Type

float

Remarks

If @n < 0 then KSccdf = 1.

If @x < 0 then KSccdf = 1.

Examples

SELECT n,

       sqrt(18.0 / n) as x,

       wct.KSCCDF(n, sqrt(18.0 / n)) as ks

FROM

(

    VALUES

        (50.0),

        (100.0),

        (500.0),

        (1000.0),

        (5000.0),

        (10000.0),

        (50000.0),

        (10E5),

        (10E6),

        (10E7),

        (10E8)

) p (n);

This produces the following result.

{"columns":[{"field":"n","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"x","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"},{"field":"ks","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"n":"50","x":"0.6","ks":"9.6340704561422E-18"},{"n":"100","x":"0.424264068711929","ks":"7.60653219848608E-17"},{"n":"500","x":"0.189736659610103","ks":"3.09340954271647E-16"},{"n":"1000","x":"0.134164078649987","ks":"3.69599264243387E-16"},{"n":"5000","x":"0.06","ks":"4.33712332368773E-16"},{"n":"10000","x":"0.0424264068711929","ks":"4.44862619998983E-16"},{"n":"50000","x":"0.0189736659610103","ks":"4.56828378005821E-16"},{"n":"1000000","x":"0.00424264068711928","ks":"4.62531376662394E-16"},{"n":"10000000","x":"0.00134164078649987","ks":"4.63483518913332E-16"},{"n":"100000000","x":"0.000424264068711929","ks":"4.63772741835367E-16"},{"n":"1000000000","x":"0.000134164078649987","ks":"4.63863011932784E-16"}]}