C++ named requirements:
RandomNumberDistribution (since C++11)

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 and

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

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