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/* gdtr.c
*
* Gamma distribution function
*
*
*
* SYNOPSIS:
*
* double a, b, x, y, gdtr();
*
* y = gdtr( a, b, x );
*
*
*
* DESCRIPTION:
*
* Returns the integral from zero to x of the Gamma probability
* density function:
*
*
* x
* b -
* a | | b-1 -at
* y = ----- | t e dt
* - | |
* | (b) -
* 0
*
* The incomplete Gamma integral is used, according to the
* relation
*
* y = igam( b, ax ).
*
*
* ACCURACY:
*
* See igam().
*
* ERROR MESSAGES:
*
* message condition value returned
* gdtr domain x < 0 0.0
*
*/
/* gdtrc.c
*
* Complemented Gamma distribution function
*
*
*
* SYNOPSIS:
*
* double a, b, x, y, gdtrc();
*
* y = gdtrc( a, b, x );
*
*
*
* DESCRIPTION:
*
* Returns the integral from x to infinity of the Gamma
* probability density function:
*
*
* inf.
* b -
* a | | b-1 -at
* y = ----- | t e dt
* - | |
* | (b) -
* x
*
* The incomplete Gamma integral is used, according to the
* relation
*
* y = igamc( b, ax ).
*
*
* ACCURACY:
*
* See igamc().
*
* ERROR MESSAGES:
*
* message condition value returned
* gdtrc domain x < 0 0.0
*
*/
/* gdtr() */
/*
* 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;
// $$y = \frac{a^b}{\Gamma(b)}\,\int_0^x{t^{b-1}\,e^{-a\,t}\,dt}$$
pub fn gdtr(a: f64, b: f64, x: f64) -> f64 {
//! Gamma distribution function
//!
//! ## DESCRIPTION:
//!
//! Returns the integral from zero to x of the Gamma probability
//! density function:
//!
#![doc=include_str!("gdtr.svg")]
//!
//! The incomplete Gamma integral is used, according to the
//! relation
//!
//! `y = igam( b, ax )`
//!
//!
//! ## ACCURACY:
//!
//! See [`cephes64::igam`](crate::cephes64::igam).
if x < 0.0 {
//sf_error("gdtr", SF_ERROR_DOMAIN, NULL);
f64::NAN
} else {
igam(b, a * x)
}
}
// $$y = \frac{a^b}{\Gamma(b)}\,\int_x^{\infty}{t^{b-1}\,e^{-a\,t}\,dt}$$
pub fn gdtrc(a: f64, b: f64, x: f64) -> f64 {
//! Complemented Gamma distribution function
//!
//! ## DESCRIPTION:
//!
//! Returns the integral from x to infinity of the Gamma
//! probability density function:
//!
#![doc=include_str!("gdtrc.svg")]
//!
//! The incomplete Gamma integral is used, according to the
//! relation
//!
//! `y = igamc( b, ax )`
//!
//! ## ACCURACY:
//!
//! See [`cephes64::igamc`](crate::cephes64::igamc).
if x < 0.0 {
//sf_error("gdtrc", SF_ERROR_DOMAIN, NULL);
f64::NAN
} else {
igamc(b, a * x)
}
}
pub fn gdtri(a: f64, b: f64, y: f64) -> f64 {
//! Inverse gamma distribution function
if y < 0.0 || y > 1.0 || a <= 0.0 || b < 0.0 {
//sf_error("gdtri", SF_ERROR_DOMAIN, NULL);
f64::NAN
} else {
igamci(b, 1.0 - y) / a
}
}
// Very few tests due to simplicity of implementation
#[cfg(test)]
mod gdtr_tests {
use super::*;
#[test]
fn gdtr_trivials() {
assert_eq!(gdtrc(0.0, 0.0, 0.0).is_nan(), true);
assert_eq!(gdtrc(0.1, 0.0, 0.0).is_nan(), true);
assert_eq!(gdtr(0.0, 1.0, 1.0), 0.0);
assert_eq!(gdtr(1.0, 0.0, 1.0), 1.0); // TODO: Is this right?
assert_eq!(gdtr(1.0, 1.0, -1e-10).is_nan(), true);
assert_eq!(gdtri(0.0, 1.0, 1.0).is_nan(), true);
assert_eq!(gdtri(1.0, 0.0, 1.0), f64::INFINITY);
assert_eq!(gdtri(1.0, 1.0, 0.0), 0.0);
assert_eq!(gdtri(1.0, 1.0, 1.0 + 1e-10).is_nan(), true);
assert_eq!(gdtri(1.0, 1.0, 1.0), f64::INFINITY);
}
#[test]
fn gdtr_tests() {
assert_eq!(gdtrc(1.0, 1.0, 1.0), 0.36787944117144245);
assert_eq!(gdtrc(1.0, 1.0, 0.0), 1.0);
assert_eq!(gdtrc(2.0, 3.0, 4.0), 0.013753967744002971);
assert_eq!(gdtr(1.0, 1.0, 1.0), 0.6321205588285577);
assert_eq!(gdtr(1.0, 1.0, 0.0), 0.0);
assert_eq!(gdtr(2.0, 3.0, 4.0), 0.986246032255997);
assert_eq!(gdtri(1.0, 1.0, 0.3), 0.35667494393873245);
assert_eq!(gdtri(1.0, 1.0, 0.6), 0.9162907318741551);
assert_eq!(gdtri(2.0, 3.0, 0.8), 2.139514930062667);
assert_eq!(gdtri(2.0, 3.0, 0.9999), 6.964085309003543);
}
}