GammaCHI: A package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral)

Abstract
A Fortran 90 module GammaCHI for computing and inverting the gamma and chi-square cumulative distribution functions (central and noncentral) is presented. The main novelty of this package is the reliable and accurate inversion routines for the noncentral cumulative distribution functions. Additionally, the package also provides routines for computing the gamma function, the error function and other functions related to the gamma function. The module includes the routines cdfgamC, invcdfgamC, ...

Title of program: Module GammaCHI
Catalogue Id: AEVM_v1_0

Nature of problem
The computation and inversion of gamma and chi-square cumulative distribution functions (central and noncentral) as well as the computation of the error and gamma functions is needed in many problems of applied and mathematical physics.

Versions of this program held in the CPC repository in Mendeley Data
AEVM_v1_0; Module GammaCHI; 10.1016/j.cpc.2015.01.004
AEVM_v1_0; Module GammaCHI; 10.1016/j.cpc.2015.01.004

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

# 摘要
本文提出一款用于计算与逆求解伽马分布（gamma distribution）及卡方分布（chi-square distribution）（中心与非中心形式）累积分布函数（cumulative distribution function）的Fortran 90模块GammaCHI。本程序包的核心创新点在于针对非中心累积分布函数的可靠且高精度的逆计算例程（inversion routines）。此外，该程序包还提供伽马函数（gamma function）、误差函数（error function）及其他与伽马函数相关的计算例程。本模块包含cdfgamC、invcdfgamC等计算例程。

## 程序标题：GammaCHI模块
## 目录标识：AEVM_v1_0

## 问题需求
在应用物理与数学物理的诸多问题中，均需对伽马分布与卡方分布的累积分布函数（中心与非中心形式）进行计算与逆求解，同时也需要误差函数与伽马函数的计算功能。

## 门德利数据（Mendeley Data）的CPC仓库收录的本程序版本：
AEVM_v1_0; GammaCHI模块; 10.1016/j.cpc.2015.01.004
AEVM_v1_0; GammaCHI模块; 10.1016/j.cpc.2015.01.004

本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2018）。