std::student_t_distribution(3)

NAME
std::student_t_distribution - std::student_t_distribution

Synopsis
   Defined in header <random>
   template< class RealType = double > (since C++11)
   class student_t_distribution;
   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 constructs new distribution
   (C++11) (public member function)
   reset resets the internal state of the distribution
   (C++11) (public member function)

Generation
   operator() generates the next random number in the distribution
   (C++11) (public member function)

Characteristics
   n returns the n distribution parameter (degrees of freedom)
                 (public member function)
   param gets or sets the distribution parameter object
   (C++11) (public member function)
   min returns the minimum potentially generated value
   (C++11) (public member function)
   max returns the maximum potentially generated value
   (C++11) (public member function)

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