26 Numerics library [numerics]

26.5 Random number generation [rand]

26.5.8 Random number distribution class templates [rand.dist]

26.5.8.4 Poisson distributions [rand.dist.pois]

26.5.8.4.5 Class template extreme_value_distribution [rand.dist.pois.extreme]

1

An extreme_value_distribution random number distribution produces random numbers x distributed according to the probability density function280 \[% p(x\,|\,a,b) = \frac{1}{b} \cdot \exp\left( \frac{a-x}{b} \,-\, \exp\left(\frac{a-x}{b}\right) \right) \; \mbox{.} \]

template<class RealType = double>
 class extreme_value_distribution{
public:
 // types
 typedef RealType result_type;
 typedef unspecified param_type;

 // constructor and reset functions
 explicit extreme_value_distribution(RealType a = 0.0, RealType b = 1.0);
 explicit extreme_value_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 a() const;
 RealType b() const;
 param_type param() const;
 void param(const param_type& parm);
 result_type min() const;
 result_type max() const;
};

explicit extreme_value_distribution(RealType a = 0.0, RealType b = 1.0);

2

Requires: 0 < b .

3

Effects: Constructs an extreme_value_distribution object; a and b correspond to the respective parameters of the distribution.

RealType a() const;

4

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

RealType b() const;

5

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

279)

The distribution corresponding to this probability density function is also known (with a possible change of variable) as the Gumbel Type I, the log-Weibull, or the Fisher-Tippett Type I distribution.