Struct statrs::distribution::ChiSquared

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

Implements the Chi-squared distribution which is a special case of the Gamma distribution (referenced Here)

Examples

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

let n = ChiSquared::new(3.0).unwrap();
assert_eq!(n.mean().unwrap(), 3.0);
assert!(prec::almost_eq(n.pdf(4.0), 0.107981933026376103901, 1e-15));

Implementations

Constructs a new chi-squared distribution with freedom degrees of freedom. This is equivalent to a Gamma distribution with a shape of freedom / 2.0 and a rate of 0.5.

Errors

Returns an error if freedom is NaN or less than or equal to 0.0

Examples
use statrs::distribution::ChiSquared;

let mut result = ChiSquared::new(3.0);
assert!(result.is_ok());

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

Returns the degrees of freedom of the chi-squared distribution

Examples
use statrs::distribution::ChiSquared;

let n = ChiSquared::new(3.0).unwrap();
assert_eq!(n.freedom(), 3.0);

Returns the shape of the underlying Gamma distribution

Examples
use statrs::distribution::ChiSquared;

let n = ChiSquared::new(3.0).unwrap();
assert_eq!(n.shape(), 3.0 / 2.0);

Returns the rate of the underlying Gamma distribution

Examples
use statrs::distribution::ChiSquared;

let n = ChiSquared::new(3.0).unwrap();
assert_eq!(n.rate(), 0.5);

Trait Implementations

Returns a copy of the value. Read more

Performs copy-assignment from source. Read more

Calculates the probability density function for the chi-squared distribution at x

Formula
ⓘ
1 / (2^(k / 2) * Γ(k / 2)) * x^((k / 2) - 1) * e^(-x / 2)

where k is the degrees of freedom and Γ is the gamma function

Calculates the log probability density function for the chi-squared distribution at x

Formula
ⓘ
ln(1 / (2^(k / 2) * Γ(k / 2)) * x^((k / 2) - 1) * e^(-x / 2))

Calculates the cumulative distribution function for the chi-squared distribution at x

Formula
ⓘ
(1 / Γ(k / 2)) * γ(k / 2, x / 2)

where k is the degrees of freedom, Γ is the gamma function, and γ is the lower incomplete gamma function

Calculates the cumulative distribution function for the chi-squared distribution at x

Formula
ⓘ
(1 / Γ(k / 2)) * γ(k / 2, x / 2)

where k is the degrees of freedom, Γ is the gamma function, and γ is the upper incomplete gamma function

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 chi-squared distribution

Formula
ⓘ
k

where k is the degrees of freedom

Returns the variance of the chi-squared distribution

Formula
ⓘ
2k

where k is the degrees of freedom

Returns the entropy of the chi-squared distribution

Formula
ⓘ
(k / 2) + ln(2 * Γ(k / 2)) + (1 - (k / 2)) * ψ(k / 2)

where k is the degrees of freedom, Γ is the gamma function, and ψ is the digamma function

Returns the skewness of the chi-squared distribution

Formula
ⓘ
sqrt(8 / k)

where k is the degrees of freedom

Returns the standard deviation, if it exists. Read more

Returns the maximum value in the domain of the chi-squared distribution representable by a double precision float

Formula
ⓘ
INF

Returns the median of the chi-squared distribution

Formula
ⓘ
k * (1 - (2 / 9k))^3

Returns the minimum value in the domain of the chi-squared distribution representable by a double precision float

Formula
ⓘ
0

Returns the mode of the chi-squared distribution

Formula
ⓘ
k - 2

where k is the degrees of freedom

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

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason. Read more

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

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

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.