/C++

# std::student_t_distribution

Defined in header <random>
template< class RealType = double >
class student_t_distribution;
(since C++11)

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 the type of the parameter set, see RandomNumberDistribution.

### 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)

### Non-member functions

 operator==operator!= compares two distribution objects (function) operator<> performs stream input and output on pseudo-random number distribution (function template)

### Example

Weisstein, Eric W. "Student's t-Distribution." From MathWorld--A Wolfram Web Resource.