skewness Interface

public interface skewness

Calculates the sample skewness of a set of values given in a vector of any size with one dimension applying the following equation:

$$S_{x} = \frac{n}{\left( n-1 \right)\left( n-2 \right) }\sum\limits_{i=1}^{n}\left( \frac{x_{i}-\overline{x} }{\sigma_{x}} \right)^3$$

Where:

• $x$ is a vector with real numbers.
• $n$ is how many numbers are included in $x$.

Syntax

y = skewness(x)

Where:

• x = vector of rank 1 with real numbers. See this example to use an array of rank larger than 1.
• y = real number of the same kind as x with the sample skewness of x.

Example

The following program calculates the sample skewness of a vector:

 PROGRAM skewnessExample
    USE FU_Statistics, ONLY: skewness
    IMPLICIT NONE
    REAL, DIMENSION(5) :: x = [1., 2., 3., 4., 5.]
    WRITE(*,*) skewness(x)
 END PROGRAM skewnessExample

Module Procedures