26 Numerics library [numerics]

26.5 Random number generation [rand]

26.5.8 Random number distribution class templates [rand.dist] Normal distributions [rand.dist.norm] Class template student_t_distribution [rand.dist.norm.t]

A student_t_distribution random number distribution produces random numbers x distributed according to the probability density function \[%
      =  \frac{1}
              {\sqrt{n \pi}}
         \cdot \frac{\Gamma\big((n+1)/2\big)}
         \cdot \left( 1+\frac{x^2}{n} \right) ^ {-(n+1)/2}
\; \mbox{.}

template<class RealType = double>
 class student_t_distribution{
 // types
 typedef RealType result_type;
 typedef unspecified param_type;

 // constructor and reset functions
 explicit student_t_distribution(RealType n = 1);
 explicit student_t_distribution(const param_type& parm);
 void reset();

 // generating functions
 template<class URNG>
   result_type operator()(URNG& g);
 template<class URNG>
   result_type operator()(URNG& g, const param_type& parm);

 // property functions
 RealType n() const;
 param_type param() const;
 void param(const param_type& parm);
 result_type min() const;
 result_type max() const;

explicit student_t_distribution(RealType n = 1);

Requires: 0 < n .

Effects: Constructs a student_t_distribution object; n corresponds to the parameter of the distribution.

RealType n() const;

Returns: The value of the n parameter with which the object was constructed.