crow

Utility library

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Statistics

Crow Library by Ross Smith

#include "crow/statistics.hpp"
namespace Crow;

Statistics class

template <std::floating_point T = double> class Statistics;

A Statistics object keeps running statistics for one or two variables.

Member functions with anx_ or y_ prefix return the statistics for that variable. The versions with no prefix are synonyms for the x_ version, for convenience when only one variable is being tallied.

Based on code by John Cook:

• Standard deviation
• Skewness and kurtosis
• Linear regression

constexpr Statistics::Statistics() noexcept;
constexpr Statistics::Statistics(const Statistics& s) noexcept;
constexpr Statistics::Statistics(Statistics&& s) noexcept;
constexpr Statistics::~Statistics() noexcept;
constexpr Statistics& Statistics::operator=(const Statistics& s) noexcept;
constexpr Statistics& Statistics::operator=(Statistics&& s) noexcept;

Life cycle functions.

constexpr Statistics& Statistics::operator()(T x) noexcept;
constexpr Statistics& Statistics::operator()(T x, T y) noexcept;

The function call operator adds a new value, or a new pair of values, to the statistics. Calling stats(x) is equivalent to stats(x,0), but skips redundant arithmetic.

constexpr Statistics Statistics::operator+(const Statistics& s) const noexcept;
constexpr Statistics& Statistics::operator+=(const Statistics& s) noexcept;

The addition operators combine sets of statistics.

constexpr void Statistics::clear() noexcept;

Resets all statistics o their initial empty state.

constexpr int Statistics::n() const noexcept;
constexpr T Statistics::tn() const noexcept;

Return the number of items entered, as an integer or a floating point number.

constexpr T Statistics::min() const noexcept;
constexpr T Statistics::x_min() const noexcept;
constexpr T Statistics::y_min() const noexcept;
constexpr T Statistics::max() const noexcept;
constexpr T Statistics::x_max() const noexcept;
constexpr T Statistics::y_max() const noexcept;

Return the minimum and maximum values. These will return zero if n<1.

constexpr T Statistics::mean() const noexcept;
constexpr T Statistics::x_mean() const noexcept;
constexpr T Statistics::y_mean() const noexcept;

Return the mean values. These will return zero if n<1.

constexpr T Statistics::variance() const noexcept;
constexpr T Statistics::x_variance() const noexcept;
constexpr T Statistics::y_variance() const noexcept;
T Statistics::sd() const noexcept;
T Statistics::x_sd() const noexcept;
T Statistics::y_sd() const noexcept;
constexpr T Statistics::pop_variance() const noexcept;
constexpr T Statistics::x_pop_variance() const noexcept;
constexpr T Statistics::y_pop_variance() const noexcept;
T Statistics::pop_sd() const noexcept;
T Statistics::x_pop_sd() const noexcept;
T Statistics::y_pop_sd() const noexcept;

Return the sample (with Bessel correction) and population (no Bessel correction) variance and standard deviation. The corrected sample measures will return zero if n<2; the uncorrected population measures will return zero if n<1.

T Statistics::skewness() const noexcept;
T Statistics::x_skewness() const noexcept;
T Statistics::y_skewness() const noexcept;
T Statistics::kurtosis() const noexcept;
T Statistics::x_kurtosis() const noexcept;
T Statistics::y_kurtosis() const noexcept;

Return the skewness (third standard moment) and kurtosis (Pearson’s modified fourth moment) of the sample. All of these will return zero if n<2.

T Statistics::r() const noexcept;

Returns the Pearson coefficient of correlation. This will return zero if n<1.

T Statistics::a() const noexcept;
T Statistics::b() const noexcept;
T Statistics::inv_a() const noexcept;
T Statistics::inv_b() const noexcept;

Return the linear regression coefficients in y=a*x+b. The inv_*() functions return the inverse coefficients in x=a'*y+b'. All of these will return zero if n<1.