Defined in header <random>  

template< class RealType = double > class student_t_distribution;  (since C++11) 
Produces random floatingpoint values x, distributed according to probability density function: \(p(xn) = \frac{1}{\sqrt{n\pi} } \cdot \frac{\Gamma(\frac{n+1}{2})}{\Gamma(\frac{n}{2})} \cdot (1+\frac{x^2}{n})^{\frac{n+1}{2} } \)p(xn) =
1 
√nπ 
Γ(
 
Γ(

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.
RealType    The result type generated by the generator. The effect is undefined if this is not one of float , double , or long double . 
Member type  Definition 

result_type  RealType 
param_type  the type of the parameter set, see RandomNumberDistribution. 
constructs new distribution (public member function) 

resets the internal state of the distribution (public member function) 

Generation 

generates the next random number in the distribution (public member function) 

Characteristics 

returns the n distribution parameter (degrees of freedom) (public member function) 

gets or sets the distribution parameter object (public member function) 

returns the minimum potentially generated value (public member function) 

returns the maximum potentially generated value (public member function) 
compares two distribution objects (function) 

performs stream input and output on pseudorandom number distribution (function template) 
Weisstein, Eric W. "Student's tDistribution." From MathWorldA Wolfram Web Resource.
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