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"}]}