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/* nbdtr.c
*
* Negative binomial distribution
*
*
*
* SYNOPSIS:
*
* int k, n;
* double p, y, nbdtr();
*
* y = nbdtr( k, n, p );
*
* DESCRIPTION:
*
* Returns the sum of the terms 0 through k of the negative
* binomial distribution:
*
* k
* -- ( n+j-1 ) n j
* > ( ) p (1-p)
* -- ( j )
* j=0
*
* In a sequence of Bernoulli trials, this is the probability
* that k or fewer failures precede the nth success.
*
* The terms are not computed individually; instead the incomplete
* beta integral is employed, according to the formula
*
* y = nbdtr( k, n, p ) = incbet( n, k+1, p ).
*
* The arguments must be positive, with p ranging from 0 to 1.
*
* ACCURACY:
*
* Tested at random points (a,b,p), with p between 0 and 1.
*
* a,b Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 100000 1.7e-13 8.8e-15
* See also incbet.c.
*
*/
/*
* Cephes Math Library Release 2.3: March, 1995
* Copyright 1984, 1987, 1995 by Stephen L. Moshier
*/
use crate::cephes64::incbet::incbet;
use crate::cephes64::incbi::incbi;
pub fn nbdtrc(k: isize, n: isize, p: f64) -> f64 {
//! Complemented negative binomial distribution
//!
//! ## DESCRIPTION:
//!
//! Returns the sum of the terms k+1 to infinity of the negative
//! binomial distribution:
//!
#![doc=include_str!("nbdtrc.svg")]
//!
//! The terms are not computed individually; instead the incomplete
//! beta integral is employed, according to the formula
//!
//! `y = nbdtrc( k, n, p ) = incbet( k+1, n, 1-p )`
//!
//! The arguments must be positive, with `p` ranging from 0 to 1.
//!
//! ## ACCURACY:
//!
//! Tested at random points (`a`, `b`, `p`), with `p` between 0 and 1.
//!
//! Relative error
//!
//!<table>
//! <tr>
//! <th>Arithmetic</th>
//! <th>a, b Domain</th>
//! <th># Trials</th>
//! <th>Peak</th>
//! <th>RMS</th>
//! </tr>
//! <tr>
//! <td>IEEE</td>
//! <td>0, 100</td>
//! <td>100000</td>
//! <td>1.7e-13</td>
//! <td>8.8e-15</td>
//! </tr>
//!</table>
//!
//! See also [`cephes64::incbet`](crate::cephes64::incbet).
if !(0.0..=1.0).contains(&p) || k < 0 {
//sf_error("nbdtr", SF_ERROR_DOMAIN, NULL);
f64::NAN
} else {
let dk = k + 1;
let dn = n;
incbet(dk as f64, dn as f64, 1.0 - p)
}
}
pub fn nbdtr(k: isize, n: isize, p: f64) -> f64 {
//! Negative binomial distribution
//!
//! ## DESCRIPTION:
//!
//! Returns the sum of the terms 0 through k of the negative
//! binomial distribution:
//!
#![doc=include_str!("nbdtr.svg")]
//!
//! In a sequence of Bernoulli trials, this is the probability
//! that k or fewer failures precede the nth success.
//!
//! The terms are not computed individually; instead the incomplete
//! beta integral is employed, according to the formula
//!
//! `y = nbdtr( k, n, p ) = incbet( n, k+1, p )`
//!
//! The arguments must be positive, with p ranging from 0 to 1.
//!
//! ## ACCURACY:
//!
//! Tested at random points (`a`, `b`, `p`), with `p` between 0 and 1.
//!
//! Relative error
//!
//!<table>
//! <tr>
//! <th>Arithmetic</th>
//! <th>a, b Domain</th>
//! <th># Trials</th>
//! <th>Peak</th>
//! <th>RMS</th>
//! </tr>
//! <tr>
//! <td>IEEE</td>
//! <td>0, 100</td>
//! <td>100000</td>
//! <td>1.7e-13</td>
//! <td>8.8e-15</td>
//! </tr>
//!</table>
//!
//! See also [`cephes64::incbet`](crate::cephes64::incbet).
if !(0.0..=1.0).contains(&p) || k < 0 {
//sf_error("nbdtr", SF_ERROR_DOMAIN, NULL);
f64::NAN
} else {
let dk = k + 1;
let dn = n;
incbet(dn as f64, dk as f64, p)
}
}
pub fn nbdtri(k: isize, n: isize, p: f64) -> f64 {
//! Functional inverse of negative binomial distribution
//!
//! ## DESCRIPTION:
//!
//! Finds the argument `p` such that `nbdtr(k,n,p)` is equal to `y`.
//!
//! ## ACCURACY:
//!
//! Tested at random points (`a`, `b`, `y`), with `y` between 0 and 1.
//!
//! Relative error:
//!
//!<table>
//! <tr>
//! <th>Arithmetic</th>
//! <th>a, b Domain</th>
//! <th># Trials</th>
//! <th>Peak</th>
//! <th>RMS</th>
//! </tr>
//! <tr>
//! <td>IEEE</td>
//! <td>0, 100</td>
//! <td>100000</td>
//! <td>1.5e-14</td>
//! <td>8.5e-16</td>
//! </tr>
//!</table>
//!
//! See also [`cephes64::incbi`](crate::cephes64::incbi).
if !(0.0..=1.0).contains(&p) || k < 0 {
//sf_error("nbdtri", SF_ERROR_DOMAIN, NULL);
f64::NAN
} else {
let dk = k + 1;
let dn = n;
incbi(dn as f64, dk as f64, p)
}
}
// Very few tests due to simplicity of implementation
#[cfg(test)]
mod nbdtr_tests {
use super::*;
#[test]
fn nbdtr_trivials() {
assert_eq!(nbdtrc(-1, 10, 0.5).is_nan(), true);
assert_eq!(nbdtrc(1, 10, -1e-15).is_nan(), true);
assert_eq!(nbdtrc(1, 10, 1.0 + 1e-15).is_nan(), true);
assert_eq!(nbdtr(-1, 10, 0.5).is_nan(), true);
assert_eq!(nbdtr(1, 10, -1e-15).is_nan(), true);
assert_eq!(nbdtr(1, 10, 1.0 + 1e-15).is_nan(), true);
assert_eq!(nbdtri(-1, 10, 0.5).is_nan(), true);
assert_eq!(nbdtri(1, 10, -1e-15).is_nan(), true);
assert_eq!(nbdtri(1, 10, 1.0 + 1e-15).is_nan(), true);
}
#[test]
fn nbdtr_tests() {
assert_eq!(nbdtrc(5, 10, 0.5), 0.8491210937499999);
assert_eq!(nbdtrc(5, 10, 0.9), 0.0022496700850479973);
assert_eq!(nbdtrc(15, 10, 0.5), 0.11476147174835194);
assert_eq!(nbdtrc(15, 15, 0.1), 0.9999999644052073);
assert_eq!(nbdtrc(15, 10, 0.0), 1.0);
assert_eq!(nbdtrc(15, 10, 1.0), 0.0);
assert_eq!(nbdtr(5, 10, 0.5), 0.15087890625000008);
assert_eq!(nbdtr(5, 10, 0.9), 0.997750329914952);
assert_eq!(nbdtr(15, 10, 0.5), 0.8852385282516481);
assert_eq!(nbdtr(15, 15, 0.1), 3.559479269444176e-08);
assert_eq!(nbdtr(15, 10, 0.0), 0.0);
assert_eq!(nbdtr(15, 10, 1.0), 1.0);
assert_eq!(nbdtri(5, 10, 0.5), 0.6303295486548143);
assert_eq!(nbdtri(5, 10, 0.9), 0.7744087263163602);
assert_eq!(nbdtri(15, 10, 0.5), 0.3816135642524775);
assert_eq!(nbdtri(15, 15, 0.1), 0.36969603948477525);
assert_eq!(nbdtri(15, 10, 0.0), 0.0);
assert_eq!(nbdtri(15, 10, 1.0), 1.0);
}
}