Re: [Help-gsl] Covariance calculation in gsl

[Julien Bect]

Le 13/05/2010 08:35, Srimal Jayawardena a écrit :
> double gsl_stats_covariance (const double data1[], const size_t
> stride1, const double data2[], const size_t stride2, const size_t n)
>
> http://www.gnu.org/software/gsl/manual/html_node/Covariance.html
>
>            covar = (1/(n - 1)) \sum_{i = 1}^{n} (x_i - \Hat x) (y_i - \Hat y)
>
> Is there any particular reason for dividing with (n-1) instead of just 'n' ?
>
> Whats the reasoning behind this ?
>    

Dividing by (n-1) makes "covar" an *unbiased* estimate of the population 
covariance.

This isn't true anymore if you divide by n instead. See, for instance,

http://en.wikipedia.org/wiki/Estimation_of_covariance_matrices