Trait statrs::statistics::Statistics [−] [src]

pub trait Statistics {
    fn min(&self) -> f64;
    fn max(&self) -> f64;
    fn abs_min(&self) -> f64;
    fn abs_max(&self) -> f64;
    fn mean(&self) -> f64;
    fn geometric_mean(&self) -> f64;
    fn harmonic_mean(&self) -> f64;
    fn variance(&self) -> f64;
    fn population_variance(&self) -> f64;
    fn std_dev(&self) -> f64;
    fn population_std_dev(&self) -> f64;
    fn covariance(&self, other: &Self) -> f64;
    fn population_covariance(&self, other: &Self) -> f64;
    fn quadratic_mean(&self) -> f64;
    fn order_statistic(&mut self, order: usize) -> f64;
    fn median(&mut self) -> f64;
    fn quantile(&mut self, tau: f64) -> f64;
    fn percentile(&mut self, p: usize) -> f64;
    fn lower_quartile(&mut self) -> f64;
    fn upper_quartile(&mut self) -> f64;
    fn interquartile_range(&mut self) -> f64;
    fn ranks(&mut self, tie_breaker: RankTieBreaker) -> Vec<f64>;
}

The statistics trait provides a host of statistical utilities for analzying data sets

Required Methods

Returns the minimum value in the data

Rermarks

Returns f64::NAN if data is empty or an entry is f64::NAN

Examples

use std::f64;
use statrs::statistics::Statistics;

let x = [];
assert!(x.min().is_nan());

let y = [0.0, f64::NAN, 3.0, -2.0];
assert!(y.min().is_nan());

let z = [0.0, 3.0, -2.0];
assert_eq!(z.min(), -2.0);

Returns the maximum value in the data

Remarks

Returns f64::NAN if data is empty or an entry is f64::NAN

Examples

use std::f64;
use statrs::statistics::Statistics;

let x = [];
assert!(x.max().is_nan());

let y = [0.0, f64::NAN, 3.0, -2.0];
assert!(y.max().is_nan());

let z = [0.0, 3.0, -2.0];
assert_eq!(z.max(), 3.0);

Returns the minimum absolute value in the data

Rermarks

Returns f64::NAN if data is empty or an entry is f64::NAN

Examples

use std::f64;
use statrs::statistics::Statistics;

let x = [];
assert!(x.abs_min().is_nan());

let y = [0.0, f64::NAN, 3.0, -2.0];
assert!(y.abs_min().is_nan());

let z = [0.0, 3.0, -2.0];
assert_eq!(z.abs_min(), 0.0);

Returns the maximum absolute value in the data

Rermarks

Returns f64::NAN if data is empty or an entry is f64::NAN

Examples

use std::f64;
use statrs::statistics::Statistics;

let x = [];
assert!(x.abs_max().is_nan());

let y = [0.0, f64::NAN, 3.0, -2.0];
assert!(y.abs_max().is_nan());

let z = [0.0, 3.0, -2.0, -8.0];
assert_eq!(z.abs_max(), 8.0);

Evaluates the sample mean, an estimate of the population mean.

Remarks

Returns f64::NAN if data is empty or an entry is f64::NAN

Examples

#[macro_use]
extern crate statrs;

use std::f64;
use statrs::statistics::Statistics;

let x = [];
assert!(x.mean().is_nan());

let y = [0.0, f64::NAN, 3.0, -2.0];
assert!(y.mean().is_nan());

let z = [0.0, 3.0, -2.0];
assert_almost_eq!(z.mean(), 1.0 / 3.0, 1e-15);

Evaluates the geometric mean of the data

Remarks

Returns f64::NAN if data is empty or an entry is f64::NAN. Returns f64::NAN if an entry is less than 0. Returns 0 if no entry is less than 0 but there are entries equal to 0.

Examples

#[macro_use]
extern crate statrs;

use std::f64;
use statrs::statistics::Statistics;

let x = [];
assert!(x.geometric_mean().is_nan());

let y = [0.0, f64::NAN, 3.0, -2.0];
assert!(y.geometric_mean().is_nan());

let mut z = [0.0, 3.0, -2.0];
assert!(z.geometric_mean().is_nan());

z = [0.0, 3.0, 2.0];
assert_eq!(z.geometric_mean(), 0.0);

z = [1.0, 2.0, 3.0];
// test value from online calculator, could be more accurate
assert_almost_eq!(z.geometric_mean(), 1.81712, 1e-5);

Evaluates the harmonic mean of the data

Remarks

Returns f64::NAN if data is empty or an entry is f64::NAN, or if any value in data is less than 0. Returns 0 if there are no values less than 0 but there exists values equal to 0.

Examples

#[macro_use]
extern crate statrs;

use std::f64;
use statrs::statistics::Statistics;

let x = [];
assert!(x.harmonic_mean().is_nan());

let y = [0.0, f64::NAN, 3.0, -2.0];
assert!(y.harmonic_mean().is_nan());

let mut z = [0.0, 3.0, -2.0];
assert!(z.harmonic_mean().is_nan());

z = [0.0, 3.0, 2.0];
assert_eq!(z.harmonic_mean(), 0.0);

z = [1.0, 2.0, 3.0];
// test value from online calculator, could be more accurate
assert_almost_eq!(z.harmonic_mean(), 1.63636, 1e-5);

Estimates the unbiased population variance from the provided samples

Remarks

On a dataset of size N, N-1 is used as a normalizer (Bessel's correction).

Returns f64::NAN if data has less than two entries or if any entry is f64::NAN

Examples

use std::f64;
use statrs::statistics::Statistics;

let x = [];
assert!(x.variance().is_nan());

let y = [0.0, f64::NAN, 3.0, -2.0];
assert!(y.variance().is_nan());

let z = [0.0, 3.0, -2.0];
assert_eq!(z.variance(), 19.0 / 3.0);

Evaluates the population variance from a full population.

Remarks

On a dataset of size N, N is used as a normalizer and would thus be biased if applied to a subset

Returns f64::NAN if data is empty or an entry is f64::NAN

Examples

use std::f64;
use statrs::statistics::Statistics;

let x = [];
assert!(x.population_variance().is_nan());

let y = [0.0, f64::NAN, 3.0, -2.0];
assert!(y.population_variance().is_nan());

let z = [0.0, 3.0, -2.0];
assert_eq!(z.population_variance(), 38.0 / 9.0);

Estimates the unbiased population standard deviation from the provided samples

Remarks

On a dataset of size N, N-1 is used as a normalizer (Bessel's correction).

Returns f64::NAN if data has less than two entries or if any entry is f64::NAN

Examples

use std::f64;
use statrs::statistics::Statistics;

let x = [];
assert!(x.std_dev().is_nan());

let y = [0.0, f64::NAN, 3.0, -2.0];
assert!(y.std_dev().is_nan());

let z = [0.0, 3.0, -2.0];
assert_eq!(z.std_dev(), (19f64 / 3.0).sqrt());

Evaluates the population standard deviation from a full population.

Remarks

On a dataset of size N, N is used as a normalizer and would thus be biased if applied to a subset

Returns f64::NAN if data is empty or an entry is f64::NAN

Examples

use std::f64;
use statrs::statistics::Statistics;

let x = [];
assert!(x.population_std_dev().is_nan());

let y = [0.0, f64::NAN, 3.0, -2.0];
assert!(y.population_std_dev().is_nan());

let z = [0.0, 3.0, -2.0];
assert_eq!(z.population_std_dev(), (38f64 / 9.0).sqrt());

Estimates the unbiased population covariance between the two provided samples

Remarks

On a dataset of size N, N-1 is used as a normalizer (Bessel's correction).

Returns f64::NAN if data has less than two entries or if any entry is f64::NAN

Panics

If the two sample containers do not contain the same number of elements

Examples

use std::f64;
use statrs::statistics::Statistics;

let x = [];
assert!(x.covariance(&[]).is_nan());

let y1 = [0.0, f64::NAN, 3.0, -2.0];
let y2 = [-5.0, 4.0, 10.0, f64::NAN];
assert!(y1.covariance(&y2).is_nan());

let z1 = [0.0, 3.0, -2.0];
let z2 = [-5.0, 4.0, 10.0];
assert_eq!(z1.covariance(&z2), -5.5);

Evaluates the population covariance between the two provider populations

Remarks

On a dataset of size N, N is used as a normalizer and would thus be biased if applied to a subset

Returns f64::NAN if data is empty or any entry is f64::NAN

Panics

If the two sample containers do not contain the same number of elements

Examples

use std::f64;
use statrs::statistics::Statistics;

let x = [];
assert!(x.population_covariance(&[]).is_nan());

let y1 = [0.0, f64::NAN, 3.0, -2.0];
let y2 = [-5.0, 4.0, 10.0, f64::NAN];
assert!(y1.population_covariance(&y2).is_nan());

let z1 = [0.0, 3.0, -2.0];
let z2 = [-5.0, 4.0, 10.0];
assert_eq!(z1.population_covariance(&z2), -11.0 / 3.0);

Estimates the quadratic mean (Root Mean Square) of the data

Remarks

Returns f64::NAN if data is empty or any entry is f64::NAN

Examples

#[macro_use]
extern crate statrs;

use std::f64;
use statrs::statistics::Statistics;

let x = [];
assert!(x.quadratic_mean().is_nan());

let y = [0.0, f64::NAN, 3.0, -2.0];
assert!(y.quadratic_mean().is_nan());

let z = [0.0, 3.0, -2.0];
// test value from online calculator, could be more accurate
assert_almost_eq!(z.quadratic_mean(), 2.08167, 1e-5);

Returns the order statistic (order 1..N) from the data

Remarks

No sorting is assumed. Order must be one-based (between 1 and N inclusive) Returns f64::NAN if order is outside the viable range or data is empty.

Examples

use statrs::statistics::Statistics;

let mut x = [];
assert!(x.order_statistic(1).is_nan());

let mut y = [0.0, 3.0, -2.0];
assert!(y.order_statistic(0).is_nan());
assert!(y.order_statistic(4).is_nan());
assert_eq!(y.order_statistic(2), 0.0);
assert!(y != [0.0, 3.0, -2.0]);

Returns the median value from the data

Remarks

Returns f64::NAN if data is empty

Examples

use statrs::statistics::Statistics;

let mut x = [];
assert!(x.median().is_nan());

let mut y = [0.0, 3.0, -2.0];
assert_eq!(y.median(), 0.0);
assert!(y != [0.0, 3.0, -2.0]);

Estimates the tau-th quantile from the data. The tau-th quantile is the data value where the cumulative distribution function crosses tau.

Remarks

No sorting is assumed. Tau must be between 0 and 1 inclusive. Returns f64::NAN if data is empty or tau is outside the inclusive range.

Examples

use statrs::statistics::Statistics;

let mut x = [];
assert!(x.quantile(0.5).is_nan());

let mut y = [0.0, 3.0, -2.0];
assert!(y.quantile(-1.0).is_nan());
assert!(y.quantile(2.0).is_nan());
assert_eq!(y.quantile(0.5), 0.0);
assert!(y != [0.0, 3.0, -2.0]);

Estimates the p-Percentile value from the data.

Remarks

Use quantile for non-integer percentiles. p must be between 0 and 100 inclusive. Returns f64::NAN if data is empty or p is outside the inclusive range.

Examples

use statrs::Statistics;

let mut x = [];
assert!(x.percentile(0).is_nan());

let mut y = [1.0, 5.0, 3.0, 4.0, 10.0, 9.0, 6.0, 7.0, 8.0, 2.0];
assert_eq!(y.percentile(0), 1.0);
assert_eq!(y.percentile(50), 5.5);
assert_eq!(y.percentile(100), 10.0);
assert!(y.percentile(105).is_nan());
assert!(y != [1.0, 5.0, 3.0, 4.0, 10.0, 9.0, 6.0, 7.0, 8.0, 2.0]);

Estimates the first quartile value from the data.

Remarks

Returns f64::NAN if data is empty

Examples

#[macro_use]
extern crate statrs;

use statrs::statistics::Statistics;

let mut x = [];
assert!(x.lower_quartile().is_nan());

let mut y = [2.0, 1.0, 3.0, 4.0];
assert_almost_eq!(y.lower_quartile(), 1.416666666666666, 1e-15);
assert!(y != [2.0, 1.0, 3.0, 4.0]);

Estimates the third quartile value from the data.

Remarks

Returns f64::NAN if data is empty

Examples

#[macro_use]
extern crate statrs;

use statrs::statistics::Statistics;

let mut x = [];
assert!(x.lower_quartile().is_nan());

let mut y = [2.0, 1.0, 3.0, 4.0];
assert_almost_eq!(y.upper_quartile(), 3.5833333333333333, 1e-15);
assert!(y != [2.0, 1.0, 3.0, 4.0]);

Estimates the inter-quartile range from the data.

Remarks

Returns f64::NAN if data is empty

Examples

#[macro_use]
extern crate statrs;

use statrs::statistics::Statistics;

let mut x = [];
assert!(x.interquartile_range().is_nan());

let mut y = [2.0, 1.0, 3.0, 4.0];
assert_almost_eq!(y.interquartile_range(), 2.166666666666667, 1e-15);
assert!(y != [2.0, 1.0, 3.0, 4.0]);

Evaluates the rank of each entry of the data.

Examples

use statrs::statistics::{Statistics, RankTieBreaker};

let mut x = [];
assert_eq!(x.ranks(RankTieBreaker::Average).len(), 0);

let y = [1.0, 3.0, 2.0, 2.0];
assert_eq!((&mut y.clone()).ranks(RankTieBreaker::Average), [1.0, 4.0, 2.5, 2.5]);
assert_eq!((&mut y.clone()).ranks(RankTieBreaker::Min), [1.0, 4.0, 2.0, 2.0]);

Implementors