std::student_t_distribution
From cppreference.com
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) =
·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.
Contents 
Member types
Member type  Definition 
result_type

RealType 
param_type

the type of the parameter set, unspecified 
Member functions
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) 
Nonmember functions
compares two distribution objects (function)  
performs stream input and output on pseudorandom number distribution (function template) 
Example
This section is incomplete Reason: no example 
External links
Weisstein, Eric W. "Student's tDistribution." From MathWorldA Wolfram Web Resource.