Struct statrs::distribution::Pareto

pub struct Pareto { /* fields omitted */ }

Implements the Pareto distribution

Examples

use statrs::distribution::{Pareto, Continuous};
use statrs::statistics::Distribution;
use statrs::prec;

let p = Pareto::new(1.0, 2.0).unwrap();
assert_eq!(p.mean().unwrap(), 2.0);
assert!(prec::almost_eq(p.pdf(2.0), 0.25, 1e-15));

Implementations

impl Pareto

pub fn new(scale: f64, shape: f64) -> Result<Pareto>

Constructs a new Pareto distribution with scale scale, and shape shape.

Errors

Returns an error if any of scale or shape are NaN. Returns an error if scale <= 0.0 or shape <= 0.0

Examples

use statrs::distribution::Pareto;

let mut result = Pareto::new(1.0, 2.0);
assert!(result.is_ok());

result = Pareto::new(0.0, 0.0);
assert!(result.is_err());

pub fn scale(&self) -> f64

Returns the scale of the Pareto distribution

Examples

use statrs::distribution::Pareto;

let n = Pareto::new(1.0, 2.0).unwrap();
assert_eq!(n.scale(), 1.0);

pub fn shape(&self) -> f64

Returns the shape of the Pareto distribution

Examples

use statrs::distribution::Pareto;

let n = Pareto::new(1.0, 2.0).unwrap();
assert_eq!(n.shape(), 2.0);

Trait Implementations

impl Clone for Pareto

fn clone(&self) -> Pareto

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Continuous<f64, f64> for Pareto

fn pdf(&self, x: f64) -> f64

Calculates the probability density function for the Pareto distribution at x

Formula

if x < x_m {
    0
} else {
    (α * x_m^α)/(x^(α + 1))
}

where x_m is the scale and α is the shape

fn ln_pdf(&self, x: f64) -> f64

Calculates the log probability density function for the Pareto distribution at x

Formula

if x < x_m {
    -INF
} else {
    ln(α) + α*ln(x_m) - (α + 1)*ln(x)
}

where x_m is the scale and α is the shape

impl ContinuousCDF<f64, f64> for Pareto

fn cdf(&self, x: f64) -> f64

Calculates the cumulative distribution function for the Pareto distribution at x

Formula

if x < x_m {
    0
} else {
    1 - (x_m/x)^α
}

where x_m is the scale and α is the shape

fn inverse_cdf(&self, p: T) -> K

Due to issues with rounding and floating-point accuracy the default implementation may be ill-behaved. Specialized inverse cdfs should be used whenever possible. Performs a binary search on the domain of cdf to obtain an approximation of F^-1(p) := inf { x | F(x) >= p }. Needless to say, performance may may be lacking.

impl Debug for Pareto

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Distribution<f64> for Pareto

fn mean(&self) -> Option<f64>

Returns the mean of the Pareto distribution

Formula

if α <= 1 {
    INF
} else {
    (α * x_m)/(α - 1)
}

where x_m is the scale and α is the shape

fn variance(&self) -> Option<f64>

Returns the variance of the Pareto distribution

Formula

if α <= 2 {
    INF
} else {
    (x_m/(α - 1))^2 * (α/(α - 2))
}

where x_m is the scale and α is the shape

fn entropy(&self) -> Option<f64>

Returns the entropy for the Pareto distribution

Formula

ln(α/x_m) - 1/α - 1

where x_m is the scale and α is the shape

fn skewness(&self) -> Option<f64>

Returns the skewness of the Pareto distribution

Panics

If α <= 3.0

where α is the shape

Formula

    (2*(α + 1)/(α - 3))*sqrt((α - 2)/α)

where α is the shape

fn std_dev(&self) -> Option<T>

Returns the standard deviation, if it exists.

impl Distribution<f64> for Pareto

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T> where
    R: Rng, 

Create an iterator that generates random values of T, using rng as the source of randomness.

impl Max<f64> for Pareto

fn max(&self) -> f64

Returns the maximum value in the domain of the Pareto distribution representable by a double precision float

Formula

INF

impl Median<f64> for Pareto

fn median(&self) -> f64

Returns the median of the Pareto distribution

Formula

x_m*2^(1/α)

where x_m is the scale and α is the shape

impl Min<f64> for Pareto

fn min(&self) -> f64

Returns the minimum value in the domain of the Pareto distribution representable by a double precision float

Formula

x_m

where x_m is the scale

impl Mode<Option<f64>> for Pareto

fn mode(&self) -> Option<f64>

Returns the mode of the Pareto distribution

Formula

x_m

where x_m is the scale

impl PartialEq<Pareto> for Pareto

fn eq(&self, other: &Pareto) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Pareto) -> bool

This method tests for !=.

impl Copy for Pareto

impl StructuralPartialEq for Pareto