system-random-effect-0.1.2.0: Random number generation for extensible effects.

System.Random.Effect

Description

A random number effect, using a pure mersenne twister under the hood. This should be plug-and-play with any application making use of extensible effects.

Patches, even for the smallest of documentation bugs, are always welcome!

Synopsis

# Documentation

data Random Source

A pure mersenne twister pseudo-random number generator.

Instances

 Typeable Random

# Seeding

Create a random number generator from a `Word64` seed.

mkRandomIO :: Member (Lift IO) r => Eff r RandomSource

Create a new random number generator, using the clocktime as the base for the seed. This must be called from a computation with a lifted base effect of `IO`.

# Running

runRandomState :: Random -> Eff (State Random :> r) w -> Eff r wSource

Runs an effectful random computation, returning the computation's result.

# Uniform Distributions

Arguments

 :: Member (State Random) r => Integer a -> Integer b -> Eff r Integer

Generates a uniformly distributed random number in the inclusive range [a, b].

Arguments

 :: Member (State Random) r => Double a -> Double b -> Eff r Double

Generates a uniformly distributed random number in the inclusive range [a, b].

NOTE: This code might not be correct, in that the returned value may not be perfectly uniformly distributed. If you know how to make one of these a better way, PLEASE send me a pull request. I just stole this implementation from the C++11 random header.

# Bernoulli Distributions

Arguments

 :: Member (State Random) r => Rational k: The fraction of results which should be true. -> Eff r Bool

Produces random boolean values, according to a discrete probability.

k must be in the range [0, 1].

Arguments

 :: Member (State Random) r => Int t -> Rational p -> Eff r Int

The value obtained is the number of successes in a sequence of t yes/no experiments, each of which succeeds with probability p.

t must be >= 0 p must be in the range [0, 1].

Warning: NOT IMPLEMENTED!

Arguments

 :: Member (State Random) r => Rational p -> Integer k -> Eff r Integer

The value represents the number of failures in a series of independent yes/no trials (each succeeds with probability p), before exactly k successes occur.

p must be in the range (0, 1] k must be >= 0

Warning: NOT IMPLEMENTED!

Arguments

 :: Member (State Random) r => Rational p -> Eff r Integer

The value represents the number of yes/no trials (each succeeding with probability p) which are necessary to obtain a single success.

`geometricDist` p is equivalent to negativeBinomialDist 1 p

p must be in the range (0, 1]

Warning: NOT IMPLEMENTED!

# Poisson Distributions

Arguments

 :: Member (State Random) r => Double μ -> Eff r Double i

The value obtained is the probability of exactly i occurrences of a random event if the expected, mean number of its occurrence under the same conditions (on the same time/space interval) is μ.

Warning: NOT IMPLEMENTED!

Arguments

 :: Member (State Random) r => Double λ. Scale parameter. -> Eff r Double

The value obtained is the time/distance until the next random event if random events occur at constant rate λ per unit of time/distance. For example, this distribution describes the time between the clicks of a Geiger counter or the distance between point mutations in a DNA strand.

This is the continuous counterpart of `geometricDist`.

Arguments

 :: Member (State Random) r => Double α. The shape parameter. -> Double β. The scale parameter. -> Eff r Double

For floating-point α, the value obtained is the sum of independent exponentially distributed random variables, each of which has a mean of β.

Arguments

 :: Member (State Random) r => Double α. The shape parameter. -> Double β. The scale parameter. -> Eff r Double

???

Warning: NOT IMPLEMENTED!

Arguments

 :: Member (State Random) r => Double α. The shape parameter. -> Double β. The scale parameter. -> Eff r Double

???

Warning: NOT IMPLEMENTED!

# Normal Distributions

Arguments

 :: Member (State Random) r => Double μ. The mean. -> Double σ. The standard deviation. -> Eff r Double

Generates random numbers as sampled from the normal distribution.

Arguments

 :: Member (State Random) r => Double μ. The mean. -> Double σ. The standard deviation. -> Eff r Double

Generates a log-normally distributed random number. This is based off of sampling the normal distribution, and then following the instructions at http://en.wikipedia.org/wiki/Log-normal_distribution#Generating_log-normally_distributed_random_variates.

Arguments

 :: Member (State Random) r => Int n. The number of degrees of freedom. -> Eff r Double

Produces random numbers according to a chi-squared distribution.

Arguments

 :: Member (State Random) r => Double Central point -> Double Scale parameter (full width half maximum) -> Eff r Double

Produced random numbers according to a Cauchy (or Lorentz) distribution.

Arguments

 :: Member (State Random) r => Int m -> Int n -> Eff r Double

Produces random numbers according to an F-distribution.

m and n are the degrees of freedom.

Arguments

 :: Member (State Random) r => Double The number of degrees of freedom -> Eff r Double

This distribution is used when estimating the mean of an unknown normally distributed value given n+1 independent measurements, each with additive errors of unknown standard deviation, as in physical measurements. Or, alternatively, when estimating the unknown mean of a normal distribution with unknown standard deviation, given n+1 samples.

# Sampling Distributions

Contains a sorted list of cumulative probabilities, so we can do a sample by generating a uniformly distributed random number in the range [0, 1), and binary searching the vector for where to put it.

Performs O(n) work building a table which we can later use sample with `discreteDist`.

Given a pre-build `DiscreteDistributionHelper` (use `buildDDH`), produces random integers on the interval [0, n), where the probability of each individual integer i is defined as w_i/S, that is the weight of the ith integer divided by the sum of all n weights.

i.e. This function produces an integer with probability equal to the weight given in its index into the parameter to `buildDDH`.

Arguments

 :: Member (State Random) r => [Double] Intervals -> DiscreteDistributionHelper Weights -> Eff r Double

This function produces random floating-point numbers, which are uniformly distributed within each of the several subintervals [b_i, b_(i+1)), each with its own weight w_i. The set of interval boundaries and the set of weights are the parameters of this distribution.

For example, `piecewiseConstantDist [ 0, 1, 10, 15 ] (buildDDH [ 1, 0, 1 ])` will produce values between 0 and 1 half the time, and values between 10 and 15 the other half of the time.

# Raw Generators

randomInt :: Member (State Random) r => Eff r IntSource

Yield a new `Int` value from the generator. The full 64 bits will be used on a 64 bit machine.

Yield a new `Int64` value from the generator.

randomWord :: Member (State Random) r => Eff r WordSource

Yield a new `Word` value from the generator.

Yield a new `Word64` value from the generator.

Yield a new 53-bit precise `Double` value from the generator. The returned number will be in the range [0, 1).

randomBits :: (Bits x, Member (State Random) r) => Eff r xSource

Yields a set of random from the internal generator, using `randomWord64` internally.

Arguments

 :: Member (State Random) r => Int The number of bits to generate -> Eff r [Bool]

Returns a list of bits which have been randomly generated.