Next: Absolute deviation, Up: Statistics [Index]

- Function:
*double***gsl_stats_mean***(const double*`data`[], size_t`stride`, size_t`n`) This function returns the arithmetic mean of

`data`, a dataset of length`n`with stride`stride`. The arithmetic mean, or*sample mean*, is denoted by*\Hat\mu*and defined as,\Hat\mu = (1/N) \sum x_i

where

*x_i*are the elements of the dataset`data`. For samples drawn from a gaussian distribution the variance of*\Hat\mu*is*\sigma^2 / N*.

- Function:
*double***gsl_stats_variance***(const double*`data`[], size_t`stride`, size_t`n`) This function returns the estimated, or

*sample*, variance of`data`, a dataset of length`n`with stride`stride`. The estimated variance is denoted by*\Hat\sigma^2*and is defined by,\Hat\sigma^2 = (1/(N-1)) \sum (x_i - \Hat\mu)^2

where

*x_i*are the elements of the dataset`data`. Note that the normalization factor of*1/(N-1)*results from the derivation of*\Hat\sigma^2*as an unbiased estimator of the population variance*\sigma^2*. For samples drawn from a Gaussian distribution the variance of*\Hat\sigma^2*itself is*2 \sigma^4 / N*.This function computes the mean via a call to

`gsl_stats_mean`

. If you have already computed the mean then you can pass it directly to`gsl_stats_variance_m`

.

- Function:
*double***gsl_stats_variance_m***(const double*`data`[], size_t`stride`, size_t`n`, double`mean`) This function returns the sample variance of

`data`relative to the given value of`mean`. The function is computed with*\Hat\mu*replaced by the value of`mean`that you supply,\Hat\sigma^2 = (1/(N-1)) \sum (x_i - mean)^2

- Function:
*double***gsl_stats_sd***(const double*`data`[], size_t`stride`, size_t`n`) - Function:
*double***gsl_stats_sd_m***(const double*`data`[], size_t`stride`, size_t`n`, double`mean`) The standard deviation is defined as the square root of the variance. These functions return the square root of the corresponding variance functions above.

- Function:
*double***gsl_stats_tss***(const double*`data`[], size_t`stride`, size_t`n`) - Function:
*double***gsl_stats_tss_m***(const double*`data`[], size_t`stride`, size_t`n`, double`mean`) These functions return the total sum of squares (TSS) of

`data`about the mean. For`gsl_stats_tss_m`

the user-supplied value of`mean`is used, and for`gsl_stats_tss`

it is computed using`gsl_stats_mean`

.TSS = \sum (x_i - mean)^2

- Function:
*double***gsl_stats_variance_with_fixed_mean***(const double*`data`[], size_t`stride`, size_t`n`, double`mean`) This function computes an unbiased estimate of the variance of

`data`when the population mean`mean`of the underlying distribution is known*a priori*. In this case the estimator for the variance uses the factor*1/N*and the sample mean*\Hat\mu*is replaced by the known population mean*\mu*,\Hat\sigma^2 = (1/N) \sum (x_i - \mu)^2

- Function:
*double***gsl_stats_sd_with_fixed_mean***(const double*`data`[], size_t`stride`, size_t`n`, double`mean`) This function calculates the standard deviation of

`data`for a fixed population mean`mean`. The result is the square root of the corresponding variance function.

Next: Absolute deviation, Up: Statistics [Index]