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std::student_t_distribution

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+12)n+12Γ(n2)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 (C++11) RealType
param_type (C++11) the type of the parameter set, see RandomNumberDistribution.

Member functions

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

Non-member functions

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

Example

#include <algorithm>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <map>
#include <random>
#include <vector>
 
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(0 < Height and 0 < BarWidth and 0 <= Padding and 0 <= Offset);
 
    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(*std::cbegin(s)) V; V e : s)
        qr.push_back(std::div(std::lerp(V(0), 8 * Height,
                                        (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);
        }
 
    for (draw_vbars<8, 5>(bars); const 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
Weisstein, Eric W. "Student's t-Distribution." From MathWorld — A Wolfram Web Resource.

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