Roland Conybeare
ecd019e8bb
git-subtree-dir: xo-distribution git-subtree-mainline:4e022df686git-subtree-split:036ca5d817
54 lines
1.5 KiB
C++
54 lines
1.5 KiB
C++
/* @file Normal.hpp */
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#pragma once
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#include "Distribution.hpp"
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#include <cmath>
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namespace xo {
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namespace distribution {
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/* the guassian distribution, with mean 0 and variance 1
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*/
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class Normal : public Distribution<double> {
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public:
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Normal() = default;
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/* N(0,1): mean 0, sdev 1 */
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static rp<Normal> unit() { return new Normal(); }
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/* normal probability density:
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*
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* x^2
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* -(1/2) 1/2
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* p(x) = e / (2.pi)
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*/
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static double density(double x) {
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static double c_sqrt_2pi = ::sqrt(2 * M_PI);
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return ::exp(-0.5 * x * x) / c_sqrt_2pi;
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} /*density*/
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/* cumulative distribution function for N(0,1):
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*
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* / x
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* |
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* | p(x).dx
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* |
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* / -oo
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*
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* where p(x) is the normal density function p(x) = e^[-x^2/2]
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*/
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static double cdf_impl(double x) {
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return 0.5 * std::erfc(-M_SQRT1_2 * x);
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} /*cdf_impl*/
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// ----- inherited from Distribution<double> -----
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virtual double cdf(double const & x) const override {
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return cdf_impl(x);
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} /*cdf*/
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}; /*Normal*/
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} /*namespace distribution*/
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} /*namespace xo*/
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/* end Normal.hpp */
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