-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | "Uniform RNG => Non-Uniform RNGs"
--   
--   "Collection of transforms uniform random number generators (RNGs) into
--   any of a dozen common RNGs. Each presenting several common interfaces.
--   Additionally Empirical distributions can be sampled from and tested
--   (chi-squared) against theoretical distributions."
@package random-variates
@version 0.1.3.0

module Stochastic.Tools
maybeHead :: [a] -> Maybe a
headOrElse :: a -> [a] -> a
mapTuple :: (a -> b) -> (c -> d) -> (a, c) -> (b, d)
histogram :: Double -> [Double] -> [Int]
comb :: Int -> Int -> Double
gamma :: Double -> Double
lower_incomplete_gamma :: Double -> Double -> Double
estimate_lower_gamma :: Double -> Double -> Double -> Double
stirlingsApprox :: (Floating r, Ord r) => r -> r
fac :: Int -> Integer
factorial :: [Integer]
fib :: Int -> Integer
fibinacci :: [Integer]
harmonics :: Double -> [Double]
statefully :: (g -> (a, g)) -> Int -> g -> ([a], g)
statefullyTakeWhile :: (g -> (a, g)) -> ([a] -> Bool) -> g -> ([a], g)
type Histogram = [Datagram]
data Datagram
Datagram :: Double -> Double -> Int -> Double -> Double -> Double -> Datagram
[lower_bound] :: Datagram -> Double
[upper_bound] :: Datagram -> Double
[frequency] :: Datagram -> Int
[rel_frequence] :: Datagram -> Double
[cum_frequence] :: Datagram -> Double
[slope] :: Datagram -> Double
fIHistogram :: [Double] -> Histogram
maxf :: Ord b => [b] -> b
minf :: Ord b => [b] -> b
datagramFromRaw :: Int -> Double -> [(Double, Int)] -> [Datagram]
accMap :: (b -> a -> b) -> (a -> b) -> [a] -> [b]
biFold :: (a -> a -> b) -> [a] -> [b]
dependentMap :: (a -> a -> b) -> (a -> b) -> [a] -> [b]
bin :: (Double -> Double) -> [Double] -> [(Double, Int)]
lowerOf :: Double -> Double -> Double
group :: (Ord a) => [a] -> [(a, Int)]
groupSeq :: (Eq a) => [a] -> [(a, Int)]
instance GHC.Classes.Eq Stochastic.Tools.Datagram
instance GHC.Show.Show Stochastic.Tools.Datagram

module Stochastic.Distribution.Discrete
class DiscreteDistribution g where rands n g0 = statefully (rand) n g0
rand :: DiscreteDistribution g => g -> (Int, g)
rands :: DiscreteDistribution g => Int -> g -> ([Int], g)
cdf :: DiscreteDistribution g => g -> Int -> Double
cdf' :: DiscreteDistribution g => g -> Double -> Int
pmf :: DiscreteDistribution g => g -> Int -> Double

module Stochastic.Distribution.Continuous
class ContinuousDistribution g where rands n g0 = statefully (rand) n g0 pdf g a b = (cdf g b) - (cdf g a)
rand :: ContinuousDistribution g => g -> (Double, g)
rands :: ContinuousDistribution g => Int -> g -> ([Double], g)
cdf :: ContinuousDistribution g => g -> Double -> Double
cdf' :: ContinuousDistribution g => g -> Double -> Double
pdf :: ContinuousDistribution g => g -> Double -> Double -> Double
degreesOfFreedom :: ContinuousDistribution g => g -> Int

module Stochastic.Generator
type Gen g a = g -> (a, g)
data IOGen g a
IOGen :: (g -> (a, g)) -> (MVar g) -> IOGen g a
liftGen :: (g -> (a, g)) -> g -> IO (IOGen g a)
nextIO :: IOGen g a -> IO a
foldGenWhile :: (g -> (a, g)) -> (b -> a -> b) -> b -> (b -> Bool) -> (g -> ([a], g))
genWhile :: (g -> (a, g)) -> (a -> Bool) -> (g -> ([a], g))
genTake :: (g -> (a, g)) -> Integer -> (g -> ([a], g))
dropGen :: (g -> (a, g)) -> Integer -> g -> g
dropIO :: IOGen g a -> Integer -> IO ()

module Stochastic.Uniform

-- | For information on the performance of the xorshift-128-plus PRNG,
--   please see: <a>Vigna et al.</a>
xorshift128plus :: Integer -> UniformRandom
data UniformRandom
nWayAllocate :: Integer -> Integer -> UniformRandom -> ([UniformRandom], UniformRandom)
splitAllocate :: Integer -> UniformRandom -> (UniformRandom, UniformRandom)

-- | The class <a>RandomGen</a> provides a common interface to random
--   number generators.
class RandomGen g

-- | The <a>next</a> operation returns an <a>Int</a> that is uniformly
--   distributed in the range returned by <a>genRange</a> (including both
--   end points), and a new generator.
next :: RandomGen g => g -> (Int, g)

-- | The <a>genRange</a> operation yields the range of values returned by
--   the generator.
--   
--   It is required that:
--   
--   <ul>
--   <li>If <tt>(a,b) = <a>genRange</a> g</tt>, then <tt>a &lt;
--   b</tt>.</li>
--   <li><a>genRange</a> always returns a pair of defined <a>Int</a>s.</li>
--   </ul>
--   
--   The second condition ensures that <a>genRange</a> cannot examine its
--   argument, and hence the value it returns can be determined only by the
--   instance of <a>RandomGen</a>. That in turn allows an implementation to
--   make a single call to <a>genRange</a> to establish a generator's
--   range, without being concerned that the generator returned by (say)
--   <a>next</a> might have a different range to the generator passed to
--   <a>next</a>.
--   
--   The default definition spans the full range of <a>Int</a>.
genRange :: RandomGen g => g -> (Int, Int)

-- | The <a>split</a> operation allows one to obtain two distinct random
--   number generators. This is very useful in functional programs (for
--   example, when passing a random number generator down to recursive
--   calls), but very little work has been done on statistically robust
--   implementations of <a>split</a> ([<a>System.Random\#Burton</a>,
--   <a>System.Random\#Hellekalek</a>] are the only examples we know of).
split :: RandomGen g => g -> (g, g)
instance GHC.Classes.Eq Stochastic.Uniform.EntropyExhausted
instance GHC.Exception.Exception Stochastic.Uniform.EntropyExhausted
instance GHC.Show.Show Stochastic.Uniform.EntropyExhausted
instance System.Random.RandomGen Stochastic.Uniform.UniformRandom

module Stochastic.Distributions
data UniformBase
stdBase :: Integer -> UniformBase
seededBase :: IO UniformBase
data Empirical
Empirical :: Int -> (Double -> Double) -> (Double -> Double) -> Empirical
[degreesOfFreedom] :: Empirical -> Int
[cdf] :: Empirical -> Double -> Double
[cdf'] :: Empirical -> Double -> Double
mkEmpirical :: [Double] -> Empirical

module Stochastic.Distributions.Continuous
mkUniform :: UniformBase -> Dist
mkExp :: UniformBase -> Double -> Dist
mkNormal :: UniformBase -> Double -> Double -> Dist
mkEmpirical :: UniformBase -> [Double] -> Dist
data Dist
Uniform :: UniformBase -> Dist
Exponential :: Double -> UniformBase -> Dist
Normal :: Double -> Double -> (Maybe Double) -> UniformBase -> Dist
ChiSquared :: Int -> UniformBase -> Dist
Empirical :: Empirical -> UniformBase -> Dist
class ContinuousDistribution g where rands n g0 = statefully (rand) n g0 pdf g a b = (cdf g b) - (cdf g a)
rand :: ContinuousDistribution g => g -> (Double, g)
rands :: ContinuousDistribution g => Int -> g -> ([Double], g)
cdf :: ContinuousDistribution g => g -> Double -> Double
cdf' :: ContinuousDistribution g => g -> Double -> Double
pdf :: ContinuousDistribution g => g -> Double -> Double -> Double
degreesOfFreedom :: ContinuousDistribution g => g -> Int
instance Stochastic.Distribution.Continuous.ContinuousDistribution Stochastic.Distributions.UniformBase
instance Stochastic.Distribution.Continuous.ContinuousDistribution Stochastic.Distributions.Continuous.Dist

module Stochastic.Distributions.Discrete
mkBinomial :: UniformBase -> Double -> Int -> Dist
mkBernoulli :: UniformBase -> Double -> Dist
mkPoisson :: UniformBase -> Double -> Dist
mkZipF :: UniformBase -> Int -> Double -> Dist
mkGeometric :: UniformBase -> Double -> Dist
data Dist
Uniform :: Int -> Int -> UniformBase -> Dist
Poisson :: Dist -> Dist
Geometric :: Double -> UniformBase -> Dist
Bernoulli :: Double -> UniformBase -> Dist
Binomial :: Int -> Double -> DiscreteCache -> UniformBase -> Dist
ZipF :: Int -> Double -> DiscreteCache -> UniformBase -> Dist
class DiscreteDistribution g where rands n g0 = statefully (rand) n g0
rand :: DiscreteDistribution g => g -> (Int, g)
rands :: DiscreteDistribution g => Int -> g -> ([Int], g)
cdf :: DiscreteDistribution g => g -> Int -> Double
cdf' :: DiscreteDistribution g => g -> Double -> Int
pmf :: DiscreteDistribution g => g -> Int -> Double
instance Stochastic.Distribution.Discrete.DiscreteDistribution Stochastic.Distributions.Discrete.Dist

module Stochastic.Analysis
chiSquaredTest :: (ContinuousDistribution g) => g -> Empirical -> [Double] -> Double
discreteChiSquaredTest :: (DiscreteDistribution g) => g -> Empirical -> [Int] -> Double