Struct statrs::distribution::NegativeBinomial

pub struct NegativeBinomial { /* private fields */ }

Implements the negative binomial distribution.

Please note carefully the meaning of the parameters. As noted in the wikipedia article, there are several different commonly used conventions for the parameters of the negative binomial distribution.

The negative binomial distribution is a discrete distribution with two parameters, r and p. When r is an integer, the negative binomial distribution can be interpreted as the distribution of the number of failures in a sequence of Bernoulli trials that continue until r successes occur. p is the probability of success in a single Bernoulli trial.

NegativeBinomial accepts non-integer values for r. This is a generalization of the more common case where r is an integer.

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

impl NegativeBinomial

pub fn new(r: f64, p: f64) -> Result<NegativeBinomial>

Constructs a new negative binomial distribution with parameters r and p. When r is an integer, the negative binomial distribution can be interpreted as the distribution of the number of failures in a sequence of Bernoulli trials that continue until r successes occur. p is the probability of success in a single Bernoulli trial.

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());

pub fn p(&self) -> f64

Returns the probability of success p of a single Bernoulli trial associated with the negative binomial distribution.

Examples

use statrs::distribution::NegativeBinomial;

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

pub fn r(&self) -> f64

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

impl Clone for NegativeBinomial

fn clone(&self) -> NegativeBinomial

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for NegativeBinomial

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

Formats the value using the given formatter.

impl Discrete<u64, f64> for NegativeBinomial

fn pmf(&self, x: u64) -> f64

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

Formula

When r is an integer, the formula is:

(x + r - 1 choose x) * (1 - p)^x * p^r

The general formula for real r is:

Γ(r + x)/(Γ(r) * Γ(x + 1)) * (1 - p)^x * p^r

where Γ(x) is the Gamma function.

fn ln_pmf(&self, x: u64) -> f64

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

Formula

When r is an integer, the formula is:

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

The general formula for real r is:

ln(Γ(r + x)/(Γ(r) * Γ(x + 1)) * (1 - p)^x * p^r)

where Γ(x) is the Gamma function.

impl DiscreteCDF<u64, f64> for NegativeBinomial

fn cdf(&self, x: u64) -> f64

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

Formula

I_(p)(r, x+1)

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

fn sf(&self, x: u64) -> f64

Calculates the survival 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

I_(1-p)(x+1, r)

where I_(x)(a, b) is the regularized incomplete beta function

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.

impl DiscreteDistribution<f64> for NegativeBinomial

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

Returns the mean of the negative binomial distribution.

Formula

r * (1-p) / p

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

Returns the variance of the negative binomial distribution.

Formula

r * (1-p) / p^2

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

Returns the skewness of the negative binomial distribution.

Formula

(2-p) / sqrt(r * (1-p))

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

Returns the standard deviation, if it exists.

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

Returns the entropy, if it exists.

impl Distribution<u64> for NegativeBinomial

fn sample<R: Rng + ?Sized>(&self, r: &mut R) -> u64

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.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S> where
    F: Fn(T) -> S, 

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

impl Max<u64> for NegativeBinomial

fn max(&self) -> u64

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

Formula

u64::MAX

impl Min<u64> for NegativeBinomial

fn min(&self) -> u64

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

Formula

0

impl Mode<Option<f64>> for NegativeBinomial

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

Returns the mode for the negative binomial distribution.

Formula

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

impl PartialEq<NegativeBinomial> for NegativeBinomial

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

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

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

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

impl Copy for NegativeBinomial

impl StructuralPartialEq for NegativeBinomial