Which non-uniform random number generators should be in the standard?

[Beliavsky]

Random normal deviates are commonly needed and are available in many other scientific computing languages, such as Matlab, R, Python/Numpy, Julia, and C++, so I think Fortran should also have a random_normal() subroutine, analogous to random_number().

[certik]

I think this would be a good fit for stdlib, would you mind proposing it there?

[Beliavsky]

@certik
I think people are already working on non-uniform RNG, including normal deviates, in stdlib, for example fortran-lang/stdlib#240 . There are many known statistical distributions to sample from, and I'm not sure that everything that will be implemented in stdlib should be in the standard, but I think normal variates should be.

[Beliavsky]

According to a post by John D. Cook, the C++ standard includes

Generating from non-uniform distributions
Distributions directly supported
Bernoulli
Binomial
Exponential
Gamma
Geometric
Normal (Gaussian)
Poisson

but not
Cauchy
Chi squared
Student t
Snedecor F
Weibull
Rayleigh

Distributions that can be sampled easily, if not very efficiently, given a normal RNG, may not be needed in the standard -- examples are the Student's t and chi-squared distributions.

[Beliavsky]

Here are links to lists of non-uniform RNG in R, NumPy, SciPy, Matlab statistics toolbox

[peteroupc]

According to a post by John D. Cook, the C++ standard includes

Generating from non-uniform distributions
Distributions directly supported
Bernoulli
Binomial
Exponential
Gamma
Geometric
Normal (Gaussian)
Poisson

but not
Cauchy
Chi squared
Student t
Snedecor F
Weibull
Rayleigh

That post refers to the Technical Report 1 extensions of C++, which predated C++11 which introduced <random> and its distributions for the first time in the main standard. In C++11, of the distributions listed here, only the Rayleigh distribution is not offered there.

[johnwcowan]

The proposal for the next Scheme standard
specifies the following generators:

Uniform generators

• arbitrary integer bounds
• integer bounds in the ranges of `uint1 uint8 int8 uint16 int16 uint32 int32 uint64 int64
• real numbers with arbitrary bounds
• complex numbers with arbitrary rectangular or polar bounds
• booleans
• characters drawn from a string with replacement
• strings whose characters are drawn from a string with replacement and whose lengths are uniformly distributed between 0 and an upper bound.

Non-uniform distributions

• Bernoulli
• binomial
• categorical (given a vector of weights)
• normal
• exponential
• geometric
• Poisson
• Zipf.

Generators of fixed-length vectors

• uniformly from the surface or interior of an n-sphere
• uniformly from the surface of an n-ellipsoid