KURTOSIS_P

Updated 2024-02-13 19:28:48.973000

Syntax

SELECT [westclintech].[wct].[KURTOSIS_P] (
  <@Known_x, float,>)

Description

Use the aggregate function KURTOSIS_P to calculate the kurtosis for an entire population. The KURTOSIS_P function is an implementation of the kurtosis “excess” as formulated by Abramowitz and Stegun in Handboook of Mathematical Functions, 26.1.16.

\gamma_2=\frac{\mu_4}{\mu_2}-3

Arguments

@Known_x

the values to be used in the calculation. @Known_x must be of a type float or of a type that implicitly converts to float.

Return Type

float

Remarks

If you want to measure the kurtosis for a sample, then use the KURTOSIS_S function.

To calculate the population skewness use the SKEWNESS_P function.

To calculate the sample skewness use the SKEWNESS_S function.

Examples

SELECT wct.KURTOSIS_P(x) as KURTOSIS_P

FROM

(

    SELECT 30000.0000216303

    UNION ALL

    SELECT 30000.0000565854

    UNION ALL

    SELECT 30000.000038137

    UNION ALL

    SELECT 30000.0000495983

    UNION ALL

    SELECT 30000.0000185861

    UNION ALL

    SELECT 30000.0000863479

    UNION ALL

    SELECT 30000.0000776366

    UNION ALL

    SELECT 30000.0000637985

    UNION ALL

    SELECT 30000.0000939786

    UNION ALL

    SELECT 30000.000031191

    UNION ALL

    SELECT 30000.0000550457

    UNION ALL

    SELECT 30000.0000207558

    UNION ALL

    SELECT 30000.0000805531

    UNION ALL

    SELECT 30000.0000241287

) n(x);

This produces the following result

            KURTOSIS_P
----------------------
     -1.34100844093842

In this example, we generate 100 random numbers form the standard normal distribution using the wct.SeriesFloat function and calculate the population kurtosis.

SELECT wct.KURTOSIS_P(k.SeriesValue) as KURTOSIS_P

FROM wctMath.wct.SeriesFloat(0, 1, NULL, 100, 'N') k;

This produces the following result (your results will be different).

{"columns":[{"field":"KURTOSIS_P","headerClass":"ag-right-aligned-header","cellClass":"ag-right-aligned-cell"}],"rows":[{"KURTOSIS_P":"-0.0599061758404065"}]}