Struct statrs::distribution::NegativeBinomial

pub struct NegativeBinomial { /* private fields */ }

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

impl NegativeBinomial

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

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());

pub fn p(&self) -> f64

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);

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

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

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

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))

impl DiscreteCDF<u64, f64> for NegativeBinomial

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

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

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, Self: Sized,

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, Self: Sized,

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