Math-GSL

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lib/Math/GSL/Statistics.pm  view on Meta::CPAN


=item * C<gsl_stats_correlation($data1, $stride1, $data2, $stride2, $n)> - This function efficiently computes the Pearson correlation coefficient between the array reference $data1 and $data2 which must both be of the same length $n.
 r = cov(x, y) / (\Hat\sigma_x \Hat\sigma_y)
   = {1/(n-1) \sum (x_i - \Hat x) (y_i - \Hat y)
      \over
      \sqrt{1/(n-1) \sum (x_i - \Hat x)^2} \sqrt{1/(n-1) \sum (y_i - \Hat y)^2}
     }

=item * C<gsl_stats_variance_m($data, $stride, $n, $mean)> - This function returns the sample variance of $data, an array reference, relative to the given value of $mean. The function is computed with \Hat\mu replaced by the value of mean that you su...

=item * C<gsl_stats_absdev_m($data, $stride, $n, $mean)> - This function computes the absolute deviation of the dataset $data, an array refrence, relative to the given value of $mean, absdev  = (1/N) \sum |x_i - mean|. This function is useful if you ...

=item * C<gsl_stats_wmean($w, $wstride, $data, $stride, $n)> - This function returns the weighted mean of the dataset $data array reference with stride $stride and length $n, using the set of weights $w, which is an array reference, with stride $wstr...

=item * C<gsl_stats_wvariance($w, $wstride, $data, $stride, $n)> - This function returns the estimated variance of the dataset $data, which is the dataset, with stride $stride and length $n, using the set of weights $w (as an array reference) with st...

=item * C<gsl_stats_wvariance_m($w, $wstride, $data, $stride, $n, $wmean, $wsd)> - This function returns the estimated variance of the weighted dataset $data (which is an array reference) using the given weighted mean $wmean.

=item * C<gsl_stats_wsd($w, $wstride, $data, $stride, $n)> - The standard deviation is defined as the square root of the variance. This function returns the square root of the corresponding variance function gsl_stats_wvariance above.

=item * C<gsl_stats_wsd_m($w, $wstride, $data, $stride, $n, $wmean)> - This function returns the square root of the corresponding variance function gsl_stats_wvariance_m above.

=item * C<gsl_stats_wvariance_with_fixed_mean($w, $wstride, $data, $stride, $n, $mean)> - This function computes an unbiased estimate of the variance of weighted dataset $data (which is an array reference) when the population mean $mean of the underl...

=item * C<gsl_stats_wsd_with_fixed_mean($w, $wstride, $data, $stride, $n, $mean)> - The standard deviation is defined as the square root of the variance. This function returns the square root of the corresponding variance function above.

=item * C<gsl_stats_wtss($w, $wstride, $data, $stride, $n)>

=item * C<gsl_stats_wtss_m($w, $wstride, $data, $stride, $n, $wmean)> - These functions return the weighted total sum of squares (TSS) of data about the weighted mean. For gsl_stats_wtss_m the user-supplied value of $wmean is used, and for gsl_stats_...

=item * C<gsl_stats_wabsdev($w, $wstride, $data, $stride, $n)> - This function computes the weighted absolute deviation from the weighted mean of $data, which is an array reference. The absolute deviation from the mean is defined as, absdev = (\sum w...

=item * C<gsl_stats_wabsdev_m($w, $wstride, $data, $stride, $n, $wmean)> - This function computes the absolute deviation of the weighted dataset $data (an array reference) about the given weighted mean $wmean.

=item * C<gsl_stats_wskew($w, $wstride, $data, $stride, $n)> - This function computes the weighted skewness of the dataset $data, an array reference. skew = (\sum w_i ((x_i - xbar)/\sigma)^3) / (\sum w_i)

=item * C<gsl_stats_wskew_m_sd($w, $wstride, $data, $stride, $n, $wmean, $wsd)> - This function computes the weighted skewness of the dataset $data using the given values of the weighted mean and weighted standard deviation, $wmean and $wsd.

=item * C<gsl_stats_wkurtosis($w, $wstride, $data, $stride, $n)> - This function computes the weighted kurtosis of the dataset $data, an array reference. kurtosis = ((\sum w_i ((x_i - xbar)/sigma)^4) / (\sum w_i)) - 3

=item * C<gsl_stats_wkurtosis_m_sd($w, $wstride, $data, $stride, $n, $wmean, $wsd)> - This function computes the weighted kurtosis of the dataset $data, an array reference, using the given values of the weighted mean and weighted standard deviation, ...

=item * C<gsl_stats_pvariance($data, $stride, $n, $data2, $stride2, $n2)>

=item * C<gsl_stats_ttest($data1, $stride1, $n1, $data2, $stride2, $n2)>

=item * C<gsl_stats_max($data, $stride, $n)> - This function returns the maximum value in the $data array reference, a dataset of length $n with stride $stride. The maximum value is defined as the value of the element x_i which satisfies x_i >= x_j f...

=item * C<gsl_stats_min($data, $stride, $n)> - This function returns the minimum value in $data (which is an array reference) a dataset of length $n with stride $stride. The minimum value is defined as the value of the element x_i which satisfies x_i...

=item * C<gsl_stats_minmax($data, $stride, $n)> - This function finds both the minimum and maximum values in $data, which is an array reference, in a single pass and returns them in this order.

=item * C<gsl_stats_max_index($data, $stride, $n)> - This function returns the index of the maximum value in $data array reference, a dataset of length $n with stride $stride. The maximum value is defined as the value of the element x_i which satisfi...

=item * C<gsl_stats_min_index($data, $stride, $n)> - This function returns the index of the minimum value in $data array reference, a dataset of length $n with stride $stride. The minimum value is defined as the value of the element x_i which satisfi...

=item * C<gsl_stats_minmax_index($data, $stride, $n)> - This function returns the indexes of the minimum and maximum values in $data, an array reference in a single pass. The value are returned in this order.

=item * C<gsl_stats_median_from_sorted_data($sorted_data, $stride, $n)> - This function returns the median value of $sorted_data (which is an array reference), a dataset of length $n with stride $stride. The elements of the array must be in ascending...

=item * C<gsl_stats_quantile_from_sorted_data($sorted_data, $stride, $n, $f)> - This function returns a quantile value of $sorted_data, a double-precision array reference of length $n with stride $stride. The elements of the array must be in ascendin...

=back

The following function are simply variants for int and char of the last functions:

=over 4

=item * C<gsl_stats_int_mean >

=item * C<gsl_stats_int_variance >

=item * C<gsl_stats_int_sd >

=item * C<gsl_stats_int_variance_with_fixed_mean >

=item * C<gsl_stats_int_sd_with_fixed_mean >

=item * C<gsl_stats_int_tss >

=item * C<gsl_stats_int_tss_m >

=item * C<gsl_stats_int_absdev >

=item * C<gsl_stats_int_skew >

=item * C<gsl_stats_int_kurtosis >

=item * C<gsl_stats_int_lag1_autocorrelation >

=item * C<gsl_stats_int_covariance >

=item * C<gsl_stats_int_correlation >

=item * C<gsl_stats_int_variance_m >

=item * C<gsl_stats_int_sd_m >

=item * C<gsl_stats_int_absdev_m >

=item * C<gsl_stats_int_skew_m_sd >

=item * C<gsl_stats_int_kurtosis_m_sd >

=item * C<gsl_stats_int_lag1_autocorrelation_m >

=item * C<gsl_stats_int_covariance_m >

=item * C<gsl_stats_int_pvariance >

=item * C<gsl_stats_int_ttest >

=item * C<gsl_stats_int_max >

=item * C<gsl_stats_int_min >

=item * C<gsl_stats_int_minmax >

=item * C<gsl_stats_int_max_index >

=item * C<gsl_stats_int_min_index >



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