std::student_t_distribution

 

C++

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Pseudo-random number generation

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Random number distributions Uniform distributions uniform_int_distribution (C++11) uniform_real_distribution (C++11) generate_canonical (C++11) Bernoulli distributions bernoulli_distribution (C++11) binomial_distribution (C++11) negative_binomial_distribution (C++11) geometric_distribution (C++11) Poisson distributions poisson_distribution (C++11) exponential_distribution (C++11) gamma_distribution (C++11) weibull_distribution (C++11) extreme_value_distribution (C++11) Normal distributions normal_distribution (C++11) lognormal_distribution (C++11) chi_squared_distribution (C++11) cauchy_distribution (C++11) fisher_f_distribution (C++11) student_t_distribution (C++11) Sampling distributions discrete_distribution (C++11) piecewise_constant_distribution (C++11) piecewise_linear_distribution (C++11)

 

std::student_t_distribution

Member functions

student_t_distribution::student_t_distribution

student_t_distribution::reset

Generation

student_t_distribution::operator()

Characteristics

student_t_distribution::n

student_t_distribution::param

student_t_distribution::min

student_t_distribution::max

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 (C++11)	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 <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

External links

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