Updated: 24 May 2013

Use the aggregate function SKEWNESS_P to calculate the skewness for an entire population. The SKEWNESS_P function is an implementation of the skewness as formulated by Abramowitz and Stegun in

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**.

float

· If you want measure the skewness for a sample, then use the SKEWNESS_S function.

· To calculate the population kurtosis use the KURTOSIS_P function.

· To calculate the sample kurtosis use the KURTOSIS_S function.

SELECT wct.SKEWNESS_P(x) as SKEWNESS_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

SKEWNESS_P

----------------------

0.204132079810574

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

SELECT wct.SKEWNESS_P(k.SeriesValue) as SKEWNESS_P

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

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

SKEWNESS_P

----------------------

-0.143810928339362