Implementation:Avhz RustQuant Descriptive Statistics

Knowledge Sources	RustQuant
Domains	Mathematics, Statistics
Last Updated	2026-02-07 19:00 GMT

Overview

Concrete tool for computing descriptive statistics on vectors of floating point numbers provided by the RustQuant library.

Description

The Statistic trait defines a comprehensive set of descriptive statistical functions for vectors of floating point numbers. It is implemented for Vec<f64> and provides methods organized into several categories:

Mean functions:

• mean() -- wrapper for arithmetic_mean.
• arithmetic_mean() -- sum of elements divided by count.
• geometric_mean() -- nth root of the product of elements.
• harmonic_mean() -- reciprocal of the arithmetic mean of reciprocals.

Variance and standard deviation:

• variance() / sample_variance() -- uses Bessel's correction (divides by n-1).
• population_variance() -- divides by n.
• standard_deviation() / sample_standard_deviation() -- square root of sample variance.
• population_standard_deviation() -- square root of population variance.

Bivariate statistics:

• covariance(other) -- sample covariance between two vectors.
• correlation(other) -- Pearson correlation coefficient.

Shape statistics:

• skewness() -- adjusted Fisher-Pearson standardized moment coefficient.
• kurtosis() -- excess kurtosis with bias correction.

Order statistics:

• min(), max() -- extreme values.
• median() -- middle value of sorted data.
• percentile(p), quantile(q) -- interpolated order statistics (p, q in [0, 1]).
• interquartile_range() -- Q3 - Q1.
• range() -- max - min.

All methods include assertions for minimum vector length requirements (e.g., mean requires at least 1 element, standard deviation requires at least 2, skewness requires at least 3, kurtosis requires at least 4).

Usage

Use this trait whenever you need to compute summary statistics on a vector of numeric data. In quantitative finance, descriptive statistics are fundamental for analyzing return distributions, computing risk metrics, performing portfolio analysis, and evaluating the statistical properties of time series data.

Code Reference

Source Location

• Repository: RustQuant
• File: crates/RustQuant_math/src/statistic.rs
• Lines: 1-478

Signature

pub trait Statistic<T: Float> {
    fn mean(&self) -> T;
    fn arithmetic_mean(&self) -> T;
    fn geometric_mean(&self) -> T;
    fn harmonic_mean(&self) -> T;
    fn variance(&self) -> T;
    fn sample_variance(&self) -> f64;
    fn population_variance(&self) -> f64;
    fn standard_deviation(&self) -> T;
    fn sample_standard_deviation(&self) -> f64;
    fn population_standard_deviation(&self) -> f64;
    fn covariance(&self, other: &Self) -> T;
    fn correlation(&self, other: &Self) -> T;
    fn skewness(&self) -> T;
    fn kurtosis(&self) -> T;
    fn min(&self) -> T;
    fn max(&self) -> T;
    fn median(&self) -> T;
    fn percentile(&self, percentile: f64) -> T;
    fn quantile(&self, quantile: f64) -> T;
    fn interquartile_range(&self) -> T;
    fn range(&self) -> T;
}

impl Statistic<f64> for Vec<f64> { /* ... */ }

Import

use RustQuant::math::Statistic;

I/O Contract

Inputs

Name	Type	Required	Description
self	&Vec<f64>	Yes	The vector of data to compute statistics on. Must not be empty.
other	&Vec<f64>	For covariance/correlation	A second vector of equal length for bivariate statistics.
percentile	f64	For percentile()	Value in [0, 1] specifying the desired percentile.
quantile	f64	For quantile()	Value in [0, 1] specifying the desired quantile.

Outputs

Name	Type	Description
mean()	f64	Arithmetic mean of the vector elements.
variance()	f64	Sample variance (Bessel-corrected).
standard_deviation()	f64	Sample standard deviation.
covariance()	f64	Sample covariance between two vectors.
correlation()	f64	Pearson correlation coefficient in [-1, 1].
skewness()	f64	Adjusted skewness of the distribution.
kurtosis()	f64	Excess kurtosis of the distribution.
median()	f64	Median value of the sorted data.

Usage Examples

use RustQuant::math::Statistic;

let data = vec![1.0, 2.0, 3.0, 4.0, 5.0];

// Central tendency
let mean = data.arithmetic_mean();     // 3.0
let geo = data.geometric_mean();       // ~2.605
let harm = data.harmonic_mean();       // ~2.190
let med = data.median();               // 3.0

// Dispersion
let var = data.variance();             // 2.5 (sample variance)
let pop_var = data.population_variance(); // 2.0
let sd = data.standard_deviation();    // ~1.581

// Order statistics
let mn = data.min();                   // 1.0
let mx = data.max();                   // 5.0
let rng = data.range();               // 4.0
let iqr = data.interquartile_range();  // Q3 - Q1
let p50 = data.percentile(0.5);       // median

// Bivariate statistics
let x = vec![2.1, 2.5, 4.0, 3.6];
let y = vec![8.0, 10.0, 12.0, 14.0];
let cov = x.covariance(&y);           // 2.0
let corr = x.correlation(&y);         // ~0.864

Related Pages

• Principle:Avhz_RustQuant_Descriptive_Statistics