Struct statrs::distribution::Pareto

source · [−]
pub struct Pareto { /* private fields */ }
Expand description

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

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());

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);

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

Returns a copy of the value. Read more

Performs copy-assignment from source. Read more

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

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

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

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. Read more

Formats the value using the given formatter. Read more

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

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

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F Read more

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

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

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

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

Returns the standard deviation, if it exists. Read more

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

Formula
ⓘ
INF

Returns the median of the Pareto distribution

Formula
ⓘ
x_m*2^(1/α)

where x_m is the scale and α is the shape

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

Returns the mode of the Pareto distribution

Formula
ⓘ
x_m

where x_m is the scale

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

This method tests for !=.

Auto Trait Implementations

Blanket Implementations

Gets the TypeId of self. Read more

Immutably borrows from an owned value. Read more

Mutably borrows from an owned value. Read more

Returns the argument unchanged.

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

Should always be Self

Performance hack: Clone doesn’t get inlined for Copy types in debug mode, so make it inline anyway.

Tests if Self the same as the type T Read more

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

Checks if self is actually part of its subset T (and can be converted to it).

Use with care! Same as self.to_subset but without any property checks. Always succeeds.

The inclusion map: converts self to the equivalent element of its superset.

The resulting type after obtaining ownership.

Creates owned data from borrowed data, usually by cloning. Read more

🔬 This is a nightly-only experimental API. (toowned_clone_into)

Uses borrowed data to replace owned data, usually by cloning. Read more

The type returned in the event of a conversion error.

Performs the conversion.

The type returned in the event of a conversion error.

Performs the conversion.