#
# = Statistics
# 1. {Mean, Standard Deviation and Variance}[link:rdoc/stats_rdoc.html#1]
# 1. {Absolute deviation}[link:rdoc/stats_rdoc.html#2]
# 1. {Higher moments (skewness and kurtosis)}[link:rdoc/stats_rdoc.html#3]
# 1. {Autocorrelation}[link:rdoc/stats_rdoc.html#4]
# 1. {Covariance}[link:rdoc/stats_rdoc.html#5]
# 1. {Correlation}[link:rdoc/stats_rdoc.html#6]
# 1. {Weighted samples}[link:rdoc/stats_rdoc.html#7]
# 1. {Maximum and minimum values}[link:rdoc/stats_rdoc.html#8]
# 1. {Median and percentiles}[link:rdoc/stats_rdoc.html#9]
# 1. {Examples}[link:rdoc/stats_rdoc.html#10]
#
# == {}[link:index.html"name="1] 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 <tt>self.mean</tt>.
# (Requires GSL 1.11)
# ---
# * GSL::Vector#tss_m(mean)
#
# Returns the total sum of squares about <tt>mean</tt>.
# (Requires GSL 1.11)
#
# ---
# * GSL::Stats::variance_m(v[, mean])
# * GSL::Vector#variance_m([mean])
#
# Variance of <tt>v</tt> relative to the given value of <tt>mean</tt>.
#
# ---
# * GSL::Stats::sd(v[, mean])
# * GSL::Vector#sd([mean])
#
# Standard deviation.
#
# ---
# * GSL::Stats::tss(v[, mean])
# * GSL::Vector#tss([mean])
#
# (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 <tt>v</tt> when the population mean
# <tt>mean</tt> of the underlying distribution is known <tt>a priori</tt>.
#
# ---
# * 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 <tt>v</tt> when the population mean
# <tt>mean</tt> of the underlying distribution is known <tt>a priori</tt>.
#
# == {}[link:index.html"name="2] Absolute deviation
# ---
# * GSL::Stats::absdev(v[, mean])
# * GSL::Vector#absdev([mean])
#
# Compute the absolute deviation (from the mean <tt>mean</tt> if given).
#
# == {}[link:index.html"name="3] 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
#
# == {}[link:index.html"name="4] Autocorrelation
# ---
# * GSL::Stats::lag1_autocorrelation(v[, mean])
# * GSL::Vector#lag1_autocorrelation([mean])
#
# The lag-1 autocorrelation
#
# == {}[link:index.html"name="5] Covariance
# ---
# * GSL::Stats::covariance(v1, v2)
# * GSL::Stats::covariance_m(v1, v2, mean1, mean2)
#
# Covariance of vectors <tt>v1, v2</tt>.
#
# == {}[link:index.html"name="6] Correlation
# ---
# * GSL::Stats::correlation(v1, v2)
#
# This efficiently computes the Pearson correlation coefficient between the vectors <tt>v1, v2</tt>. (>= GSL-1.10)
#
# == {}[link:index.html"name="7] 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)
#
#
# == {}[link:index.html"name="8] 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 <tt>data</tt> and returns them.
#
# ---
# * GSL::Stats::max_index(data)
# * GSL::Vector#max_index
#
# Return the index of the maximum value in <tt>data</tt>.
# 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 <tt>data</tt>.
# 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 <tt>data</tt>
# in a single pass.
#
#
# == {}[link:index.html"name="9] 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 <tt>GSL::Vector#sort</tt>
# 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 <tt>GSL::Vector#sort</tt>
# should always be used first.
#
# == {}[link:index.html"name="10] 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);
#
# {prev}[link:rdoc/randist_rdoc.html]
# {next}[link:rdoc/hist_rdoc.html]
#
# {Reference index}[link:rdoc/ref_rdoc.html]
# {top}[link:index.html]
#