std::student_t_distribution (3) - Linux Manuals

std::student_t_distribution: std::student_t_distribution

NAME

std::student_t_distribution - std::student_t_distribution

Synopsis

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

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

Generation

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

Characteristics

              returns the n distribution parameter (degrees of freedom)
n (public member function)
              gets or sets the distribution parameter object
param (public member function)
              returns the minimum potentially generated value
min (public member function)
              returns the maximum potentially generated value
max (public member function)

Non-member functions

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

Example

 This section is incomplete
 Reason: no example

External links

Weisstein,_Eric_W._"Student's_t-Distribution." From MathWorld--A Wolfram Web Resource.