| Common mathematical functions | |||||||||||||||||||||||||||||||
| Mathematical special functions(C++17) | |||||||||||||||||||||||||||||||
| Mathematical constants(C++20) | |||||||||||||||||||||||||||||||
| Basic linear algebra algorithms(C++26) | |||||||||||||||||||||||||||||||
| Data-parallel types (SIMD)(C++26) | |||||||||||||||||||||||||||||||
| Floating-point environment(C++11) | |||||||||||||||||||||||||||||||
| Complex numbers | |||||||||||||||||||||||||||||||
Numeric array (valarray) | |||||||||||||||||||||||||||||||
| Pseudo-random number generation | |||||||||||||||||||||||||||||||
| Bit manipulation(C++20) | |||||||||||||||||||||||||||||||
| Saturation arithmetic(C++26) | |||||||||||||||||||||||||||||||
| Factor operations | |||||||||||||||||||||||||||||||
|
| ||||||||||||||||||||||||||||||
| Interpolations | |||||||||||||||||||||||||||||||
|
| ||||||||||||||||||||||||||||||
| Generic numeric operations | |||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||
| C-style checked integer arithmetic | |||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||
|
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Member functions | ||||
| Generation | ||||
| Characteristics | ||||
| Non-member functions | ||||
(C++11)(C++11)(until C++20) | ||||
(C++11)(C++11) |
Defined in header <random> | ||
template<class RealType=double> class student_t_distribution; | (since C++11) | |
Produces random floating-point valuesx, distributed according to probability density function:
| 1 |
| √nπ |
Γ(
| ||
Γ(
|
| x2 |
| n |
| n+1 |
| 2 |
wheren is known as the number ofdegrees of freedom. This distribution is used when estimating themean of an unknown normally distributed value givenn + 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, givenn + 1 samples.
std::student_t_distribution satisfies all requirements ofRandomNumberDistribution.
Contents |
| RealType | - | The result type generated by the generator. The effect is undefined if this is not one offloat,double, orlongdouble. |
| Member type | Definition |
result_type(C++11) | RealType |
param_type(C++11) | the type of the parameter set, seeRandomNumberDistribution. |
(C++11) | constructs new distribution (public member function)[edit] |
(C++11) | resets the internal state of the distribution (public member function)[edit] |
Generation | |
(C++11) | generates the next random number in the distribution (public member function)[edit] |
Characteristics | |
| returns then distribution parameter (degrees of freedom) (public member function)[edit] | |
(C++11) | gets or sets the distribution parameter object (public member function)[edit] |
(C++11) | returns the minimum potentially generated value (public member function)[edit] |
(C++11) | returns the maximum potentially generated value (public member function)[edit] |
(C++11)(C++11)(removed in C++20) | compares two distribution objects (function)[edit] |
(C++11) | performs stream input and output on pseudo-random number distribution (function template)[edit] |
#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,constbool DrawMinMax=true){ static_assert(0< Height and0< BarWidth and0<= Padding and0<= Offset); auto cout_n=[](auto&& v,int n=1){while(n-->0)std::cout<< v;}; constauto[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){constauto q{dv.quot}, r{dv.rem};unsignedchar 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}; constint 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(constauto&[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);constint 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. |
