带参数的累积正态分布函数的逆

Inverse of Cumulative Normal Distribution Function with parameters

本文关键字：函数 正态分布 参数      更新时间：2023-10-16

我想在C++中实现等价的matlab icdf函数，我已经发现了这个有用的帖子：https://www.johndcook.com/blog/cpp_phi_inverse/.但我希望它有可选的μ和西格玛参数，就像在matlab中一样。

我应该改变什么？

灵感来自https://gist.github.com/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;
}
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