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/* pdtri()
*
* Inverse Poisson distribution
*
*
*
* SYNOPSIS:
*
* int k;
* double m, y, pdtr();
*
* m = pdtri( k, y );
*
*
*
*
* DESCRIPTION:
*
* Finds the Poisson variable x such that the integral
* from 0 to x of the Poisson density is equal to the
* given probability y.
*
* This is accomplished using the inverse Gamma integral
* function and the relation
*
* m = igamci( k+1, y ).
*
*
*
*
* ACCURACY:
*
* See igami.c.
*
* ERROR MESSAGES:
*
* message condition value returned
* pdtri domain y < 0 or y >= 1 0.0
* k < 0
*
*/
/*
* Cephes Math Library Release 2.3: March, 1995
* Copyright 1984, 1987, 1995 by Stephen L. Moshier
*/
use crate::cephes64::igam::{igam, igamc};
use crate::cephes64::igami::igamci;
pub fn pdtrc(k: f64, m: f64) -> f64 {
//! Complemented poisson distribution
//!
//! ## DESCRIPTION:
//!
//! Returns the sum of the terms k+1 to infinity of the Poisson
//! distribution:
//!
#![doc=include_str!("pdtrc.svg")]
//!
//! The terms are not summed directly; instead the incomplete
//! Gamma integral is employed, according to the formula
//!
//! `y = pdtrc( k, m ) = igam( k+1, m )`
//!
//! The arguments must both be nonnegative.
//!
//! ## ACCURACY:
//!
//! See [`cephes64::igam`](crate::cephes64::igam).
if k < 0.0 || m < 0.0 {
//sf_error("pdtrc", SF_ERROR_DOMAIN, NULL);
f64::NAN
} else if m == 0.0 {
0.0
} else {
let v = k.floor() + 1.0;
igam(v, m)
}
}
// $$\sum_{j=0}^k{e^{-m}\,\frac{m^j}{j!}}$$
pub fn pdtr(k: f64, m: f64) -> f64 {
//! Poisson distribution
//!
//! ## DESCRIPTION:
//!
//! Returns the sum of the first k terms of the Poisson
//! distribution:
//!
#![doc=include_str!("pdtr.svg")]
//!
//! The terms are not summed directly; instead the incomplete
//! Gamma integral is employed, according to the relation
//!
//! `y = pdtr( k, m ) = igamc( k+1, m )`
//!
//! The arguments must both be nonnegative.
//!
//! ## ACCURACY:
//!
//! See [`cephes64::igamc`](crate::cephes64::igamc).
if k < 0.0 || m < 0.0 {
//sf_error("pdtr", SF_ERROR_DOMAIN, NULL);
f64::NAN
} else if m == 0.0 {
1.0
} else {
let v = k.floor() + 1.0;
igamc(v, m)
}
}
pub fn pdtri(k: isize, y: f64) -> f64 {
//! Inverse Poisson distribution
//!
//! ## DESCRIPTION:
//!
//! Finds the Poisson variable `x` such that the integral
//! from `0` to `x` of the Poisson density is equal to the
//! given probability `y`.
//!
//! This is accomplished using the inverse Gamma integral
//! function and the relation
//!
//! `m = igamci( k+1, y )`
//!
//! ## ACCURACY:
//!
//! See [`cephes64::igami`](crate::cephes64::igami).
if k < 0 || !(0.0..1.0).contains(&y) {
//sf_error("pdtri", SF_ERROR_DOMAIN, NULL);
f64::NAN
} else {
let v = (k + 1) as f64;
igamci(v, y)
}
}
// Very few tests due to simplicity of implementation
#[cfg(test)]
mod pdtr_tests {
use super::*;
#[test]
fn pdtr_trivials() {
assert!(pdtrc(0.0, -1e-20).is_nan());
assert!(pdtrc(-1e-20, 0.0).is_nan());
assert_eq!(pdtrc(0.0, 0.0), 0.0);
assert_eq!(pdtrc(0.0, f64::INFINITY), 1.0);
assert!(pdtr(0.0, -1e-20).is_nan());
assert!(pdtr(-1e-20, 0.0).is_nan());
assert_eq!(pdtr(0.0, 0.0), 1.0);
assert_eq!(pdtr(0.0, f64::INFINITY), 0.0);
assert!(pdtri(0, -1e-20).is_nan());
assert!(pdtri(-1, 0.0).is_nan());
assert!(pdtri(0, 1.0).is_nan()); // TODO: Should this be infinity?
assert_eq!(pdtri(0, 0.0), f64::INFINITY); // TODO: Should this be 0?
}
#[test]
fn pdtr_tests() {
assert_eq!(pdtrc(1.5, 3.0), 0.8008517265285442);
assert_eq!(pdtrc(3.0, 1.5), 0.06564245437845008);
assert_eq!(pdtr(1.5, 3.0), 0.1991482734714558);
assert_eq!(pdtr(3.0, 1.5), 0.9343575456215499);
assert_eq!(pdtri(1, 0.5), 1.6783469900166612);
assert_eq!(pdtri(3, 0.5), 3.672060748850897);
}
}