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(
| ||
Γ(
|
⎜
⎝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
| compares two distribution objects (function) |
|
| performs stream input and output on pseudo-random number distribution (function template) |
Example
External links
Weisstein, Eric W. "Student's t-Distribution." From MathWorld--A Wolfram Web Resource.
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