Alea is a collection of utilities to work with most known probability distributions, written in pure Crystal.
Note: This project is in development state and many distributions are still missing, as well as cumulative distribution functions, so keep in mind that breaking changes may occur frequently.
Crystal compiles to really fast native code without sacrificing any of the modern programming languages standards providing a nice and clean interface.
- PRNGs implementations
- Random sampling (single/double precision)
- Cumulative Distribution Functions (single/double precision)
|Distribution||Sampling (32 / 64)||CDF (32 / 64)|
|Beta||Y Y||N N|
|Chi-Square||Y Y||Y Y|
|Exponential||Y Y||Y Y|
|F-Snedecor||Y Y||N N|
|Gamma||Y Y||Y Y|
|Laplace||Y Y||Y Y|
|Log-Normal||Y Y||Y Y|
|Normal||Y Y||Y Y|
|Poisson||N Y||N Y|
|T-Student||Y Y||N N|
|Uniform||Y Y||Y Y|
- Distribution and empirical data statistical properties
- Quantile Functions
- Add the dependency to your
dependencies: alea: github: nin93/alea
Import the library:
Random is the interface provided to perform sampling:
random = Alea::Random.new random.normal # => -0.36790519967553736 : Float64 # Append '32' to call the single-precision version random.normal32 # => 0.19756398 : Float32
It also accepts an initial seed to reproduce the same seemingly random events across runs:
seed = 9377 random = Alea::Random.new(seed) random.exp # => 0.10203669577353723 : Float64
Plain sampling methods (such as
#gamma32) performs checks over arguments passed to prevent bad data generation or inner exceptions. In order to avoid checks (might be slow in a large data generation) you must use their unsafe version by prepending
next_ to them:
random = Alea::Random.new random.normal(loc: 0, sigma: 0) # raises Alea::UndefinedError: sigma is 0 or negative. random.next_normal(loc: 0, sigma: 0) # these might raise internal exceptions.
Timings are definitely comparable, though: see the benchmarks for direct comparisons between these methods.
Random is actually a wrapper over a well defined pseudo-random number generator. The basic generation of integers and floats comes from the underlying engine, more specifically from:
#next_u32, returning a random
#next_u64, returning a random
UInt64. Floats are obtained by
ldexp (load exponent) operations upon generated unsigned integers; signed integers are obtained by raw cast.
Currently implemented engines:
XSR128backed by xoroshiro128++ (32/64 bit)
XSR256backed by xoshiro256++ (32/64 bit)
The digits in the class name stand for the storage of their state in bits. Their period is
2^128 -1 for
2^256 -1 for
These engines are from the xoshiro (XOR/shift/rotate) collection, designed by Sebastiano Vigna and David Blackman: really fast generators promising exquisite statistical properties as well.
By default, the PRNG in use by
XSR128. You can, though, pass the desired engine as an argument to the constructor. Here is an example using
random = Alea::Random.new(Alea::XSR256) random.float # => 0.6533582874035311 : Float64 random.prng # => Alea::XSR256 # Or seeded as well random = Alea::Random.new(193, Alea::XSR256) random.float # => 0.4507930323670787 : Float64
All PRNGs in this library inherit from
PRNG. You are allowed to build your own custom PRNG by inheriting the above parent class and defining the methods needed by
Alea::Random to ensure proper repeatability and sampling, as described in this example.
It is worth noting that in these implementations
#next_u64 depend on different states and thus they are independent from each other, as well as
#next_i64. It is still fine, though, if both
#next_u64 rely on the same state, if you want. I choose not to, as it makes state advancements unpredictable.
Cumulative Distribution Functions
CDF is the interface used to calculate the Cumulative Distribution Functions. Given X ~ D and a fixed quantile x, CDFs are defined as the functions that associate x to the probability that the real-valued random X from the distribution D will take a value less or equal to x.
Arguments passed to
CDF methods to shape the distributions are analogous to those used for sampling:
Alea::CDF.normal(0.0) # => 0.5 : Float64 Alea::CDF.normal(2.0, loc: 1.0, sigma: 0.5) # => 0.9772498680518208 : Float64 Alea::CDF.chisq(5.279, df: 5.0) # => 0.6172121213841358 : Float64 Alea::CDF.chisq32(5.279, df: 5.0) # => 0.61721206 : Float32
Documentation is hosted on GitHub Pages.
Fully listed in LICENSE.md:
Randommodule for uniform sampling
randommodule for pseudo-random sampling methods
randommodule for ziggurat methods
- IncGammaBeta.jl for incomplete gamma functions
- Fork it (https://github.com/nin93/alea/fork)
- Create your feature branch (
git checkout -b my-new-feature)
- Commit your changes (
git commit -am 'Add some feature')
- Push to the branch (
git push origin my-new-feature)
- Create a new Pull Request
- Elia Franzella - creator and maintainer
- 2 months ago
- April 20, 2020
Sat, 28 Nov 2020 22:19:27 GMT