std::student_t_distribution

 

C++

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normal_distribution (C++11)

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student_t_distribution (C++11)

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std::student_t_distribution

Member functions

student_t_distribution::student_t_distribution (C++11)

student_t_distribution::reset (C++11)

Generation

student_t_distribution::operator() (C++11)

Characteristics

student_t_distribution::n (C++11)

student_t_distribution::param (C++11)

student_t_distribution::min (C++11)

student_t_distribution::max (C++11)

Non-member functions

operator==operator!= (C++11)(C++11)(until C++20)

operator<<operator>> (C++11)(C++11)

 

Defined in header <random>
template< class RealType = double > class student_t_distribution;		(since C++11)

Produces random floating-point values x, distributed according to probability density function:

\(p(x|n) = \frac{1}{\sqrt{n\pi} } \cdot \frac{\Gamma(\frac{n+1}{2})}{\Gamma(\frac{n}{2})} \cdot (1+\frac{x^2}{n})^{-\frac{n+1}{2} } \)p(x|n) =

1

√nπ

·

Γ( n+1 2 )

Γ( n 2 )

· ⎛
⎜
⎝1+

x2

n

⎞
⎟
⎠ -

n+1

2

where n is known as the number of degrees of freedom. This distribution is used when estimating the mean of an unknown normally distributed value given n+1 independent measurements, each with additive errors of unknown standard deviation, as in physical measurements. Or, alternatively, when estimating the unknown mean of a normal distribution with unknown standard deviation, given n+1 samples.

std::student_t_distribution satisfies all requirements of RandomNumberDistribution

Template parameters

RealType

-

The result type generated by the generator. The effect is undefined if this is not one of float, double, or long double.

Member types

Member type	Definition
result_type	RealType
param_type(C++11)	the type of the parameter set, see RandomNumberDistribution.

Member functions

(constructor) (C++11)	constructs new distribution (public member function)
reset (C++11)	resets the internal state of the distribution (public member function)
Generation
operator() (C++11)	generates the next random number in the distribution (public member function)
Characteristics
n	returns the n distribution parameter (degrees of freedom) (public member function)
param (C++11)	gets or sets the distribution parameter object (public member function)
min (C++11)	returns the minimum potentially generated value (public member function)
max (C++11)	returns the maximum potentially generated value (public member function)

Non-member functions

operator==operator!= (C++11)(C++11)(removed in C++20)	compares two distribution objects (function)
operator<<operator>> (C++11)	performs stream input and output on pseudo-random number distribution (function template)

Example

Run this code

#include <map>
#include <random>
#include <iomanip> 
#include <algorithm>
#include <iostream>
#include <vector>
#include <cmath>
 
template <int Height = 5, int BarWidth = 1, int Padding = 1, int Offset = 0, class Seq>
void draw_vbars(Seq&& s, const bool DrawMinMax = true) {
    static_assert((Height > 0) && (BarWidth > 0) && (Padding >= 0) && (Offset >= 0));
    auto cout_n = [](auto&& v, int n = 1) { while (n-- > 0) std::cout << v; };
    const auto [min, max] = std::minmax_element(std::cbegin(s), std::cend(s));
    std::vector<std::div_t> qr;
    for (typedef decltype(*cbegin(s)) V; V e : s)
        qr.push_back(std::div(std::lerp(V(0), Height*8, (e - *min)/(*max - *min)), 8));
    for (auto h{Height}; h-- > 0; cout_n('\n')) {
        cout_n(' ', Offset);
        for (auto dv : qr) {
            const auto q{dv.quot}, r{dv.rem};
            unsigned char d[] { 0xe2, 0x96, 0x88, 0 }; // Full Block: '█'
            q < h ? d[0] = ' ', d[1] = 0 : q == h ? d[2] -= (7 - r) : 0;
            cout_n(d, BarWidth), cout_n(' ', Padding);
        }
        if (DrawMinMax && Height > 1)
            Height - 1 == h ? std::cout << "┬ " << *max:
                          h ? std::cout << "│ "
                            : std::cout << "┴ " << *min;
    }
}
 
int main() {
    std::random_device rd{};
    std::mt19937 gen{rd()};
 
    std::student_t_distribution<> d{10.0f};
 
    const int norm = 10'000;
    const float cutoff = 0.000'3f;
 
    std::map<int, int> hist{};
    for(int n=0; n<norm; ++n) { ++hist[std::round(d(gen))]; }
 
    std::vector<float> bars;
    std::vector<int> indices;
    for (const auto& [n, p] : hist) {
        if (float x = p * (1.0f / norm); cutoff < x) {
            bars.push_back(x);
            indices.push_back(n);
        }
    }
 
    draw_vbars<8,5>(bars);
    for (int n : indices) { std::cout << " " << std::setw(2) << n << "   "; }
    std::cout << '\n';
}

Possible output:

                        █████                               ┬ 0.3753
                        █████                               │
                  ▁▁▁▁▁ █████                               │
                  █████ █████ ▆▆▆▆▆                         │
                  █████ █████ █████                         │
                  █████ █████ █████                         │
            ▄▄▄▄▄ █████ █████ █████ ▄▄▄▄▄                   │
▁▁▁▁▁ ▃▃▃▃▃ █████ █████ █████ █████ █████ ▃▃▃▃▃ ▁▁▁▁▁ ▁▁▁▁▁ ┴ 0.0049
 -4    -3    -2    -1     0     1     2     3     4     5

External links

Weisstein, Eric W. "Student's t-Distribution." From MathWorld--A Wolfram Web Resource.