带有参数的累积正态分布函数的反函数

本文介绍了带有参数的累积正态分布函数的反函数的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！ 问题描述

我想在C ++中实现等效的matlab icdf函数，我已经找到了这个有用的文章:> https ://www.johndcook/blog/cpp_phi_inverse/.但是我希望它具有可选的mu和sigma参数，如在matlab中一样.

I want to implement equivalent of matlab icdf function in C++, I have already found this useful post: www.johndcook/blog/cpp_phi_inverse/. But I want it with optional mu and sigma parameters as in matlab.

我应该改变什么?

推荐答案

灵感来自 gist.github/kmpm/1211922/6b7fcd0155b23c3dc71e6f4969f2c48785371292 :

double inverse_of_normal_cdf(const double p, const double mu, const double sigma) { if (p <= 0.0 || p >= 1.0) { std::stringstream os; os << "Invalid input argument (" << p << "); must be larger than 0 but less than 1."; throw std::invalid_argument(os.str()); } double r, val; const double q = p - 0.5; if (std::abs(q) <= .425) { r = .180625 - q * q; val = q * (((((((r * 2509.0809287301226727 + 33430.575583588128105) * r + 67265.770927008700853) * r + 45921.953931549871457) * r + 13731.693765509461125) * r + 1971.5909503065514427) * r + 133.14166789178437745) * r + 3.387132872796366608) / (((((((r * 5226.495278852854561 + 28729.085735721942674) * r + 39307.89580009271061) * r + 21213.794301586595867) * r + 5394.1960214247511077) * r + 687.1870074920579083) * r + 42.313330701600911252) * r + 1); } else { if (q > 0) { r = 1 - p; } else { r = p; } r = std::sqrt(-std::log(r)); if (r <= 5) { r += -1.6; val = (((((((r * 7.7454501427834140764e-4 + .0227238449892691845833) * r + .24178072517745061177) * r + 1.27045825245236838258) * r + 3.64784832476320460504) * r + 5.7694972214606914055) * r + 4.6303378461565452959) * r + 1.42343711074968357734) / (((((((r * 1.05075007164441684324e-9 + 5.475938084995344946e-4) * r + .0151986665636164571966) * r + .14810397642748007459) * r + .68976733498510000455) * r + 1.6763848301838038494) * r + 2.05319162663775882187) * r + 1); } else { /* very close to 0 or 1 */ r += -5; val = (((((((r * 2.01033439929228813265e-7 + 2.71155556874348757815e-5) * r + .0012426609473880784386) * r + .026532189526576123093) * r + .29656057182850489123) * r + 1.7848265399172913358) * r + 5.4637849111641143699) * r + 6.6579046435011037772) / (((((((r * 2.04426310338993978564e-15 + 1.4215117583164458887e-7) * r + 1.8463183175100546818e-5) * r + 7.868691311456132591e-4) * r + .0148753612908506148525) * r + .13692988092273580531) * r + .59983220655588793769) * r + 1); } if (q < 0.0) { val = -val; } } return mu + sigma * val; }