Asymptotic inversion of the binomial and negative binomial cumulative distribution functions

Efficient algorithms for the inversion of the cumulative central beta distribution

Accurate and efficient algorithms for the inversion of the cumulative central beta distribution are described. The algorithms are based on the combination of a fourth-order fixed point method with good non-local convergence properties (the Schwarzian-Newton method), asymptotic inversion methods and sharp bounds in the tails of the distribution function.

GammaCHI：用于伽马和卡方累积分布函数（中心和非中心）倒置与计算的软件包

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

GammaCHI软件包提供可靠且精确的非中心累积分布函数倒置算法，支持伽马、误差函数及相关函数的计算与倒置。

关于累积非中心Beta分布函数的计算与反演

On the computation and inversion of the cumulative noncentral beta distribution function

本文研究了非中心Beta分布函数$B_{p,q}(x,y)$及其互补函数的递推关系稳定性，并描述了用于计算该函数的渐近展开，同时考虑了在给定$B_{p,q}(x,y)$值时求解$x$或$y$的反问题，提供了可用于求解非线性方程（如牛顿法）的近似值。

Marcum Q函数的渐近与数值反演

The asymptotic and numerical inversion of the Marcum $Q-$function

本文提出了一种新的渐近方法用于反演广义Marcum Q函数及其互补P函数，并利用单调性和凸性性质为牛顿或割线法提供可靠的初始值，通过数值计算验证了渐近近似的可靠性。

A new asymptotic representation and inversion method for the Student's t distribution

Some special functions are particularly relevant in applied probability and statistics. For example, the incomplete beta function is the cumulative central beta distribution. In this paper, we consider the inversion of the central Student's-$t$ distribution which is a particular case of the central beta distribution. The inversion of this distribution functions is useful in hypothesis testing as well as for generating random samples distributed according to the corresponding probability density function. A new asymptotic representation in terms of the complementary error function, will be one …

Schwarzian-Newton方法用于求解非线性方程及其应用

The Schwarzian-Newton method for solving nonlinear equations, with applications

本文提出Schwarzian-Newton方法，该方法在常数Schwarzian导数下精确求解非线性方程，具有四阶收敛性，并应用于累积分布函数和椭圆积分的求逆问题。