Struct statrs::distribution::NegativeBinomial

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

Implements the NegativeBinomial distribution

Examples

use statrs::distribution::{NegativeBinomial, Discrete};
use statrs::statistics::DiscreteDistribution;
use statrs::prec::almost_eq;

let r = NegativeBinomial::new(4.0, 0.5).unwrap();
assert_eq!(r.mean().unwrap(), 4.0);
assert!(almost_eq(r.pmf(0), 0.0625, 1e-8));
assert!(almost_eq(r.pmf(3), 0.15625, 1e-8));

Implementations

Constructs a new negative binomial distribution with a given p probability of the number of successes r

Errors

Returns an error if p is NaN, less than 0.0, greater than 1.0, or if r is NaN or less than 0

Examples
use statrs::distribution::NegativeBinomial;

let mut result = NegativeBinomial::new(4.0, 0.5);
assert!(result.is_ok());

result = NegativeBinomial::new(-0.5, 5.0);
assert!(result.is_err());

Returns the probability of success p of the negative binomial distribution.

Examples
use statrs::distribution::NegativeBinomial;

let r = NegativeBinomial::new(5.0, 0.5).unwrap();
assert_eq!(r.p(), 0.5);

Returns the number r of success of this negative binomial distribution

Examples
use statrs::distribution::NegativeBinomial;

let r = NegativeBinomial::new(5.0, 0.5).unwrap();
assert_eq!(r.r(), 5.0);

Trait Implementations

Returns a copy of the value. Read more

Performs copy-assignment from source. Read more

Formats the value using the given formatter. Read more

Calculates the probability mass function for the negative binomial distribution at x

Formula
ⓘ
(x + r - 1 choose k) * (1 - p)^x * p^r

Calculates the log probability mass function for the negative binomial distribution at x

Formula
ⓘ
ln(x + r - 1 choose k) * (1 - p)^x * p^r))

Calculates the cumulative distribution function for the negative binomial distribution at x

Note that due to extending the distribution to the reals (allowing positive real values for r), while still technically a discrete distribution the CDF behaves more like that of a continuous distribution rather than a discrete distribution (i.e. a smooth graph rather than a step-ladder)

Formula
ⓘ
1 - I_(1 - p)(x + 1, r)

where I_(x)(a, b) is the regularized incomplete beta 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. Read more

Returns the mean of the negative binomial distribution

Formula
ⓘ
r * (1-p) / p

Returns the variance of the negative binomial distribution

Formula
ⓘ
r * (1-p) / p^2

Returns the skewness of the negative binomial distribution

Formula
ⓘ
(2-p) / sqrt(r * (1-p))

Returns the standard deviation, if it exists.

Returns the entropy, if it exists.

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 maximum value in the domain of the negative binomial distribution representable by a 64-bit integer

Formula
ⓘ
u64::MAX

Returns the minimum value in the domain of the negative binomial distribution representable by a 64-bit integer

Formula
ⓘ
0

Returns the mode for the negative binomial distribution

Formula
ⓘ
if r > 1 then
    floor((r - 1) * (1-p / p))
else
    0

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

Performs the conversion.

Performs the conversion.

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.