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### Class Index

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# Statistics

1. Mean, Standard Deviation and Variance

2. Absolute deviation

3. Higher moments (skewness and kurtosis)

4. Autocorrelation

5. Covariance

6. Correlation

7. Weighted samples

8. Maximum and minimum values

9. Median and percentiles

10. Examples

## Mean, Standard Deviation and Variance

- GSL::Stats::mean(v)

- GSL::Vector#mean

  Arithmetic mean.

  - Ex:

        >> require("gsl")
        => true
        >> v = Vector[1..7]
        => GSL::Vector:
        [ 1.000e+00 2.000e+00 3.000e+00 4.000e+00 5.000e+00 6.000e+00 7.000e+00 ]
        >> v.mean
        => 4.0
        >> Stats::mean(v)
        => 4.0

- GSL::Vector#tss

  Returns the total sum of squares about `self.mean`. (Requires GSL 1.11)

- GSL::Vector#tss_m(mean)

  Returns the total sum of squares about `mean`. (Requires GSL 1.11)

- GSL::Stats::variance_m(v[, mean])

- GSL::Vector#variance_m()

  Variance of `v` relative to the given value of `mean`.

- GSL::Stats::sd(v[, mean])

- GSL::Vector#sd()

  Standard deviation.

- GSL::Stats::tss(v[, mean])

- GSL::Vector#tss()

  (GSL-1.11 or later) These methods return the total sum of squares (TSS) of data about the mean.

- GSL::Stats::variance_with_fixed_mean(v, mean)

- GSL::Vector#variance_with_fixed_mean(mean)

  Unbiased estimate of the variance of `v` when the population mean `mean` of the underlying distribution is known `a priori`.

- GSL::Stats::variance_with_fixed_mean(v, mean)

- GSL::Vector#variance_with_fixed_mean(mean)

- GSL::Stats::sd_with_fixed_mean(v, mean)

- GSL::Vector#sd_with_fixed_mean(mean)

  Unbiased estimate of the variance of `v` when the population mean `mean` of the underlying distribution is known `a priori`.

## Absolute deviation

- GSL::Stats::absdev(v[, mean])

- GSL::Vector#absdev()

  Compute the absolute deviation (from the mean `mean` if given).

## Higher moments (skewness and kurtosis)

- GSL::Stats::skew(v[, mean, sd])

- GSL::Vector#skew([mean, sd])

  Skewness

- GSL::Stats::kurtosis(v[, mean, sd])

- GSL::Vector#kurtosis([mean, sd])

  Kurtosis

## Autocorrelation

- GSL::Stats::lag1_autocorrelation(v[, mean])

- GSL::Vector#lag1_autocorrelation()

  The lag-1 autocorrelation

## Covariance

- GSL::Stats::covariance(v1, v2)

- GSL::Stats::covariance_m(v1, v2, mean1, mean2)

  Covariance of vectors `v1, v2`.

## Correlation

- GSL::Stats::correlation(v1, v2)

  This efficiently computes the Pearson correlation coefficient between the vectors `v1, v2`. (>= GSL-1.10)

## Weighted samples

- GSL::Vector#wmean(w)

- GSL::Vector#wvariance(w)

- GSL::Vector#wsd(w)

- GSL::Vector#wabsdev(w)

- GSL::Vector#wskew(w)

- GSL::Vector#wkurtosis(w)

## Maximum and Minimum values

- GSL::Stats::max(data)

- GSL::Vector#max

  Return the maximum value in data.

- GSL::Stats::min(data)

- GSL::Vector#min

  Return the minimum value in data.

- GSL::Stats::minmax(data)

- GSL::Vectorminmax

  Find both the minimum and maximum values in `data` and returns them.

- GSL::Stats::max_index(data)

- GSL::Vector#max_index

  Return the index of the maximum value in `data`. The maximum value is defined as the value of the element x_i which satisfies x_i >= x_j for all j. When there are several equal maximum elements then the first one is chosen.

- GSL::Stats::min_index(data)

- GSL::Vector#min_index

  Returns the index of the minimum value in `data`. The minimum value is defined as the value of the element x_i which satisfies x_i >= x_j for all j. When there are several equal minimum elements then the first one is chosen.

- GSL::Stats::minmax_index(data)

- GSL::Vector#minmax_index

  Return the indexes of the minimum and maximum values in `data` in a single pass.

## Median and Percentiles

- GSL::Stats::median_from_sorted_data(v)

- GSL::Vector#median_from_sorted_data

  Return the median value. The elements of the data must be in ascending numerical order. There are no checks to see whether the data are sorted, so the method `GSL::Vector#sort` should always be used first.

- GSL::Stats::quantile_from_sorted_data(v)

- GSL::Vector#quantile_from_sorted_data

  Return the quantile value. The elements of the data must be in ascending numerical order. There are no checks to see whether the data are sorted, so the method `GSL::Vector#sort` should always be used first.

## Example

    #!/usr/bin/env ruby
    require 'gsl'

    ary =  [17.2, 18.1, 16.5, 18.3, 12.6]
    data = Vector.alloc(ary)
    mean     = data.mean()
    variance = data.stats_variance()
    largest  = data.stats_max()
    smallest = data.stats_min()

    printf("The dataset is %g, %g, %g, %g, %g\n",
           data[0], data[1], data[2], data[3], data[4]);

    printf("The sample mean is %g\n", mean);
    printf("The estimated variance is %g\n", variance);
    printf("The largest value is %g\n", largest);
    printf("The smallest value is %g\n", smallest);

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