C++ concepts: RandomNumberDistribution

A RandomNumberDistribution is a function object returning random numbers according to a probability density function p(x) or a discrete probability distribution P(x
i).

Requirements

The type D satisfies RandomNumberDistribution if.

• D satisfies CopyConstructible
• D satisfies CopyAssignable

Given.

• T, the type named by D::result_type
• P, the type named by D::param_type, which
• satisfies CopyConstructible
• satisfies CopyAssignable
• satisfies EqualityComparable
• has a constructor taking identical arguments as each of the constructors of D that take arguments corresponding to the distribution parameters.
• has a member function with the identical name, type, and semantics, as every member function of D that returns a parameter of the distribution
• declares a member typedef using distribution_type = D;
• d, a value of type D
• x and y, (possibly const) values of type D
• p, a (possibly const) value of type P
• g, g1, g2, lvalues of a type satisfying UniformRandomBitGenerator
• os, lvalue of a specialization of std::basic_ostream
• is, lvalue of a specialization of std::basic_istream

The following expressions must be valid and have their specified effects.

Expression	Type	Notes	Complexity
D::result_type	T	An arithmetic type	compile-time
D::param_type	P		compile-time
D()		creates a distribution indistinguishable from any other default-constructed D	constant
D(p)		creates a distribution indistinguishable from D constructed directly from the values used to construct p	Same as p's construction
d.reset()	void	Resets the internal state of the distribution. The next call to operator() on d will not depend on values produced by any engine prior to reset().	constant
x.param()	P	Returns p such that D(p).param() == p	No worse than D(p)
d.param(p)	void	Postcondition: d.param() == p	No worse than D(p)
d(g)	T	The sequence of numbers returned by successive invocations of this call with the same g are randomly distributed according to the distribution parametrized by d.param()	Amortized constant number of invocations of g
d(g,p)	T	The sequence of numbers returned by successive invocations of this call with the same g are randomly distributed according to the distribution parametrized by p	Amortized constant number of invocations of g
x.min()	T	the greatest lower bound on the values potentially returned by x’s operator(), as determined by the current values of x’s parameters	constant
x.max()	T	the least upper bound on the values potentially returned by x’s operator(), as determined by the current values of x’s parameters	constant
x == y	bool	Establishes an equivalence relation. Returns true if x.param() == y.param() and future infinite sequences of values that would be generated by repeated invocations of x(g1) and y(g2) would be equal as long as g1 == g2.	constant
x != y	bool	!(x == y)	constant
os << x	Reference to the type of os	Writes a textual representation of the distribution parameters and internal state to os. The formatting flags and fill character of os are unchanged.
is >> d	Reference to the type of is	Restores the distribution parameters and internal state with data read from is. The formatting flags of is are unchanged. The data must have been written using a stream with the same locale, CharT and Traits stream template parameters, otherwise the behavior is undefined. If bad input is encountered, is.setstate(std::ios::failbit) is called, which may throw std::ios_base::failure. d is unchanged in that case.

Notes

The parameters of a distribution object may be changed either permanently, by using d.param(p) or just for the duration of a single operator() call, by using d(g,p).

Calls to const member functions of the distribution and os << d do not affect the sequence of numbers produced by repeated d(g).

Standard library

The following standard library components satisfy RandomNumberDistribution.

uniform_int_distribution (C++11)	produces integer values evenly distributed across a range (class template)
uniform_real_distribution (C++11)	produces real values evenly distributed across a range (class template)
bernoulli_distribution (C++11)	produces bool values on a Bernoulli distribution. (class)
binomial_distribution (C++11)	produces integer values on a binomial distribution. (class template)
negative_binomial_distribution (C++11)	produces integer values on a negative binomial distribution. (class template)
geometric_distribution (C++11)	produces integer values on a geometric distribution. (class template)
poisson_distribution (C++11)	produces integer values on a poisson distribution. (class template)
exponential_distribution (C++11)	produces real values on an exponential distribution. (class template)
gamma_distribution (C++11)	produces real values on an gamma distribution. (class template)
weibull_distribution (C++11)	produces real values on a Weibull distribution. (class template)
extreme_value_distribution (C++11)	produces real values on an extreme value distribution. (class template)
normal_distribution (C++11)	produces real values on a standard normal (Gaussian) distribution. (class template)
lognormal_distribution (C++11)	produces real values on a lognormal distribution. (class template)
chi_squared_distribution (C++11)	produces real values on a chi-squared distribution. (class template)
cauchy_distribution (C++11)	produces real values on a Cauchy distribution. (class template)
fisher_f_distribution (C++11)	produces real values on a Fisher's F-distribution. (class template)
student_t_distribution (C++11)	produces real values on a Student's t-distribution. (class template)
discrete_distribution (C++11)	produces random integers on a discrete distribution. (class template)
piecewise_constant_distribution (C++11)	produces real values distributed on constant subintervals. (class template)
piecewise_linear_distribution (C++11)	produces real values distributed on defined subintervals. (class template)