# std::student_t_distribution

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< cpp‎ | numeric‎ | random

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

(constructor) | constructs new distribution (public member function)
reset | resets the internal state of the distribution (public member function)
##### Generation
operator() | generates the next random number in the distribution (public member function)
##### Characteristics
n | returns the n distribution parameter (degrees of freedom) (public member function)
param | gets or sets the distribution parameter object (public member function)
min | returns the minimum potentially generated value (public member function)
max | returns the maximum potentially generated value (public member function)

### Non-member functions

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

### Example

| This section is incomplete Reason: no example

### External links

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

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