stat_utils.H File Reference

Comprehensive statistical utilities for numeric data. More...

#include <cmath>
#include <limits>
#include <algorithm>
#include <vector>
#include <map>
#include <stdexcept>
#include <tpl_sort_utils.H>
#include <tpl_dynArray.H>

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Classes
struct	Aleph::Stats< T >
	Container for comprehensive statistical results. More...

Namespaces
namespace	Aleph
	Main namespace for Aleph-w library functions.

Functions
template<typename Container >
auto	Aleph::sum (const Container &data) -> std::decay_t< decltype(*std::begin(data))>
	Compute the sum of elements.
template<typename Container >
auto	Aleph::mean (const Container &data) -> std::decay_t< decltype(*std::begin(data))>
	Compute the arithmetic mean.
template<typename Container >
auto	Aleph::variance (const Container &data, bool population=false) -> std::decay_t< decltype(*std::begin(data))>
	Compute variance using Welford's numerically stable algorithm.
template<typename Container >
auto	Aleph::stddev (const Container &data, bool population=false) -> std::decay_t< decltype(*std::begin(data))>
	Compute standard deviation.
template<typename Container >
auto	Aleph::min_value (const Container &data) -> std::decay_t< decltype(*std::begin(data))>
	Compute minimum value.
template<typename Container >
auto	Aleph::max_value (const Container &data) -> std::decay_t< decltype(*std::begin(data))>
	Compute maximum value.
template<typename Container >
auto	Aleph::min_max (const Container &data) -> std::pair< std::decay_t< decltype(*std::begin(data))>, std::decay_t< decltype(*std::begin(data))> >
	Compute minimum and maximum values in one pass.
template<typename Container >
auto	Aleph::percentile (const Container &data, double p) -> std::decay_t< decltype(*std::begin(data))>
	Compute a percentile value.
template<typename Container >
auto	Aleph::median (const Container &data) -> std::decay_t< decltype(*std::begin(data))>
	Compute the median (50th percentile).
template<typename Container >
auto	Aleph::quartiles (const Container &data) -> std::tuple< std::decay_t< decltype(*std::begin(data))>, std::decay_t< decltype(*std::begin(data))>, std::decay_t< decltype(*std::begin(data))> >
	Compute quartiles (Q1, Q2, Q3).
template<typename Container >
auto	Aleph::iqr (const Container &data) -> std::decay_t< decltype(*std::begin(data))>
	Compute the interquartile range (IQR = Q3 - Q1).
template<typename Container >
auto	Aleph::mode (const Container &data) -> std::decay_t< decltype(*std::begin(data))>
	Compute the mode (most frequent value).
template<typename Container >
bool	Aleph::is_multimodal (const Container &data)
	Check if data is multimodal.
template<typename Container >
auto	Aleph::skewness (const Container &data) -> std::decay_t< decltype(*std::begin(data))>
	Compute skewness (measure of asymmetry).
template<typename Container >
auto	Aleph::kurtosis (const Container &data) -> std::decay_t< decltype(*std::begin(data))>
	Compute excess kurtosis (measure of tailedness).
template<typename Container >
auto	Aleph::coefficient_of_variation (const Container &data) -> std::decay_t< decltype(*std::begin(data))>
	Compute coefficient of variation (CV = stddev / mean).
template<typename Container1 , typename Container2 >
auto	Aleph::covariance (const Container1 &x, const Container2 &y, bool population=false) -> std::decay_t< decltype(*std::begin(x))>
	Compute covariance between two datasets.
template<typename Container1 , typename Container2 >
auto	Aleph::correlation (const Container1 &x, const Container2 &y) -> std::decay_t< decltype(*std::begin(x))>
	Compute Pearson correlation coefficient.
template<typename Container >
auto	Aleph::histogram (const Container &data, size_t num_bins) -> std::vector< std::pair< std::decay_t< decltype(*std::begin(data))>, size_t > >
	Compute a histogram of the data.
template<typename Container >
auto	Aleph::compute_all_stats (const Container &data) -> Stats< std::decay_t< decltype(*std::begin(data))> >
	Compute all statistics for a dataset.
template<class T >
void	Aleph::compute_stats (T *data, int l, int r, T &avg, T &var, T &med, T &_min, T &_max)
	Compute basic descriptive statistics for an array range.
template<typename Container >
void	Aleph::compute_stats (const Container &data, std::decay_t< decltype(*std::begin(data))> &avg, std::decay_t< decltype(*std::begin(data))> &var, std::decay_t< decltype(*std::begin(data))> &med, std::decay_t< decltype(*std::begin(data))> &_min, std::decay_t< decltype(*std::begin(data))> &_max)
	Compute basic descriptive statistics for a container.

Detailed Description

Comprehensive statistical utilities for numeric data.

This header provides a complete set of descriptive statistics functions for analyzing numeric data. It includes basic measures (mean, median, variance) as well as advanced statistics (skewness, kurtosis, percentiles).

Features

Basic Statistics

• Mean (average): Arithmetic mean of values
• Variance: Sample or population variance
• Standard deviation: Square root of variance
• Median: Middle value of sorted data
• Min/Max: Extreme values
• Sum: Total of all values

Advanced Statistics

• Percentiles: Arbitrary percentile (0-100)
• Quartiles: Q1, Q2 (median), Q3
• Interquartile Range (IQR): Q3 - Q1
• Mode: Most frequent value
• Coefficient of Variation: stddev/mean
• Skewness: Measure of distribution asymmetry
• Kurtosis: Measure of distribution tailedness

Data Analysis

• Histogram: Frequency distribution
• Correlation: Pearson correlation coefficient
• Covariance: Measure of joint variability

Algorithms

• Uses Welford's algorithm for numerically stable variance computation
• Quicksort for median/percentile calculations
• Single-pass algorithms where possible

Usage Example

#include <stat_utils.H>
#include <iostream>
 
std::vector<double> data = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0};
 
// Using Stats struct
auto stats = compute_all_stats(data);
std::cout << "Mean: " << stats.mean << std::endl;
std::cout << "Median: " << stats.median << std::endl;
std::cout << "Std Dev: " << stats.stddev << std::endl;
 
// Individual functions
double m = mean(data);
double p90 = percentile(data, 90);
double corr = correlation(data1, data2);

Author

Leandro Rabindranath Leon

Definition in file stat_utils.H.