covariance Interface

public interface covariance

Calculates the sample covariance between two variables given in two vectors of any size with one dimension applying the following equation:

$$\sigma_{xy} = \frac{\sum\limits_{i=1}^{n}\left(x_{i} - \overline{x}\right)\left(y_{i} - \overline{y}\right)}{n-1}$$

Where:

• $x$ and $y$ are vectors with real numbers.
• $n$ is how many numbers are included in $x$ and $y$.

Syntax

z = covariance(x,y)

Where:

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

Example

The following program calculates the covariance between two variables:

 PROGRAM covarianceExample
    USE FU_Statistics, ONLY: covariance
    IMPLICIT NONE
    REAL, DIMENSION(5) :: x = [1., 2., 3., 4., 5.]
    REAL, DIMENSION(5) :: y = [6., 7., 8., 9., 10.]
    WRITE(*,*) covariance(x, y)
 END PROGRAM covarianceExample

Module Procedures