This is a revised and updated version of the package GammaCHI. The package includes routines for computing and inverting the gamma and chi-square cumulative distribution functions (central and noncentral). Additionally, the package also provides routines for computing the gamma function, the error function and other functions related to the gamma function (the logarithm of the gamma function, the regulated gamma function and the ratio of two gamma functions). In this new version, the range of computation of the inversion routine of the central gamma distribution function invcdfgamC(ichi,a,p,q,x,ierr) is extended; p or q input values close to the underflow limit are now allowed.

New version program summary

Program Title: GammaCHI

CPC Library link to program files: https://doi.org/10.17632/d2kwwvsyny.1

Licensing provisions: GPLv2

Programming language: Fortran 90

Journal reference of previous version: Comput. Phys. Commun. 191 (2015) 132–139.

Does the new version supersede the previous version?: Yes

Reasons for the new version: With minor modifications of few of the functions included in the module GammaCHI, it is possible to enlarge the range of computation of the routine for the inversion of the central gamma distribution.

Summary of revisions: The basic algorithms are unchanged. The range of computation of the routine for the inversion of the central gamma distribution function is extended in this new version. Specifically in the routine invcdfgamC(ichi,a,p,q,x,ierr) values of p or q close to the underflow limit are now allowed.

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. For example, central and noncentral gamma distributions are used in the analysis of signal detection in different physical scenarios such as optics or quantum detection.

Solution method: Different methods of computation are used depending on the range of parameters: asymptotic expansions, quadrature methods, etc.

中文翻译：

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GammaCHI：用于反演和计算伽马和卡方累积分布函数（中心和非中心）的包。新版本公告

这是 GammaCHI 软件包的修订和更新版本。该软件包包括用于计算和求逆伽马和卡方累积分布函数（中心和非中心）的例程。此外，该包还提供用于计算伽马函数、误差函数和其他与伽马函数相关的函数（伽马函数的对数、调节伽马函数和两个伽马函数的比率）的例程。在这个新版本中，扩展了中心伽马分布函数invcdfgamC(ichi,a,p,q,x,ierr)的反演程序的计算范围；现在允许接近下溢限制的p或q输入值。

新版本程序汇总

节目名称： GammaCHI

CPC 库程序文件链接： https : //doi.org/10.17632/d2kwwvsyny.1

许可条款： GPLv2

编程语言：Fortran 90

上一版本的期刊参考： Compute。物理。社区。191 (2015) 132-139。

新版本是否取代以前的版本？：是

新版本的原因：通过对 GammaCHI 模块中包含的少数功能进行微小修改，可以扩大用于反演中心伽马分布的例程的计算范围。

修订摘要：基本算法不变。这个新版本扩展了中心伽马分布函数反演程序的计算范围。特别是在例程invcdfgamC(ichi,a,p,q,x,ierr)中，现在允许接近下溢限制的p或q值。

问题性质：伽马和卡方累积分布函数（中心和非中心）的计算和反演以及误差和伽马函数的计算在应用和数学物理的许多问题中都是需要的。例如，中心和非中心伽马分布用于不同物理场景（如光学或量子检测）中的信号检测分析。

求解方法：根据参数范围采用不同的计算方法：渐近展开法、求积法等。