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std::studen...distribution(3)  C++ Standard Libary std::studen...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 proba-
     bility
	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
	a
	nI

	A.

	I(

	n+1
	2

	)
	I(

	n
	2

	)

	A. a
	a
	a1+

	x2
	n

	a
	a
	a  -

	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  sam-
     ples.

	std::student_t_distribution  satisfies	all  requirements  of RandomNum-
     berDistribution.

Template parameters
	RealType - The result type generated by the generator. The effect is un-
     defined 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	RandomNumberDis-
     tribution.

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 <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: 'a'
		  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 << "a~ " << *max:
				h ? std::cout << "a "
				  : std::cout << "a' " << *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:
			      aaaaa				  a~ 0.3753
			      aaaaa				  a
			aaaaa aaaaa				  a
			aaaaa aaaaa aaaaa			  a
			aaaaa aaaaa aaaaa			  a
			aaaaa aaaaa aaaaa			  a
		  aaaaa aaaaa aaaaa aaaaa aaaaa 		  a
      aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa a' 0.0049
       -4    -3    -2	 -1	0     1     2	  3	4     5

External links
	Weisstein,  Eric  W. "Student's t-Distribution." From MathWorld a A Wol-
     fram Web
	Resource.

http://cppreference.com 	   2024.06.10	   std::studen...distribution(3)
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