pub trait Entropy<T> {
fn entropy(&self) -> T;
}The Entropy trait specifies an object that has a closed form solution
for its entropy
Returns the entropy. May panic depending
on the implementor.
use statrs::statistics::Entropy;
use statrs::distribution::Uniform;
let n = Uniform::new(0.0, 1.0).unwrap();
assert_eq!(0.0, n.entropy());
Returns the entropy of the bernoulli
distribution
q = (1 - p)
-q * ln(q) - p * ln(p)
Returns the entropy of the beta distribution
ln(B(α, β)) - (α - 1)ψ(α) - (β - 1)ψ(β) + (α + β - 2)ψ(α + β)
where α is shapeA, β is shapeB and ψ is the digamma function
Returns the entropy of the binomial distribution
(1 / 2) * ln (2 * π * e * n * p * (1 - p))
Returns the entropy of the categorical distribution
where p_j is the jth probability mass,
Σ is the sum from 0 to k - 1,
and k is the number of categories
Returns the entropy of the cauchy distribution
where γ is the scale
Returns the entropy of the chi distribution
Returns NaN if freedom is INF
ln(Γ(k / 2)) + 0.5 * (k - ln2 - (k - 1) * ψ(k / 2))
where k is degrees of freedom, Γ is the gamma function,
and ψ is the digamma function
Returns the entropy of the chi-squared distribution
(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 entropy of the dirichlet distribution
ln(B(α)) - (K - α_0)ψ(α_0) - Σ((α_i - 1)ψ(α_i))
where
B(α) = Π(Γ(α_i)) / Γ(Σ(α_i))
α_0 is the sum of all concentration parameters,
K is the number of concentration parameters, ψ is the digamma
function, α_i
is the ith concentration parameter, and Σ is the sum from 1 to K
Returns the entropy of the discrete uniform distribution
Returns the entropy of the erlang distribution
k - ln(λ) + ln(Γ(k)) + (1 - k) * ψ(k)
where k is the shape, λ is the rate, Γ is the gamma function,
and ψ is the digamma function
Returns the entropy of the exponential distribution
where λ is the rate
Returns the entropy of the gamma distribution
α - ln(β) + ln(Γ(α)) + (1 - α) * ψ(α)
where α is the shape, β is the rate, Γ is the gamma function,
and ψ is the digamma function
Returns the entropy of the geometric distribution
(-(1 - p) * log_2(1 - p) - p * log_2(p)) / p
Returns the entropy of the inverse gamma distribution
α + ln(β * Γ(α)) - (1 + α) * ψ(α)
where α is the shape, β is the rate, Γ is the gamma function,
and ψ is the digamma function
Returns the entropy of the log-normal distribution
ln(σe^(μ + 1 / 2) * sqrt(2π))
where μ is the location and σ is the scale
Returns the entropy of the normal distribution
(1 / 2) * ln(2σ^2 * π * e)
where σ is the standard deviation
Returns the entropy for the Pareto distribution
where x_m is the scale and α is the shape
Returns the entropy of the poisson distribution
(1 / 2) * ln(2πeλ) - 1 / (12λ) - 1 / (24λ^2) - 19 / (360λ^3)
where λ is the rate
Returns the entropy for the student’s t-distribution
If location != 0.0 && scale != 1.0
(v + 1) / 2 * (ψ((v + 1) / 2) - ψ(v / 2)) + ln(sqrt(v) * B(v / 2, 1 /
2))
where v is the freedom, ψ is the digamma function, and B is the
beta function
Returns the entropy of the triangular distribution
1 / 2 + ln((max - min) / 2)
Returns the entropy for the continuous uniform distribution
Returns the entropy of the weibull distribution
γ(1 - 1 / k) + ln(λ / k) + 1
where k is the shape, λ is the scale, and γ is
the Euler-Mascheroni constant