Safe Haskell	None
Language	Haskell2010

Factory.Math.Probability

Contents

Type-classes
Types
- Data-types
Functions

Description

AUTHOR: Dr. Alistair Ward
DESCRIPTION: Functions for probability-distributions.
CAVEAT: Because data-constructors are exposed, isValid need not be called.

Synopsis

Type-classes

class Distribution probabilityDistribution where Source #

Defines a common interface for probability-distributions.

Minimal complete definition

generatePopulation, getMean

Methods

generatePopulation :: (Fractional sample, RandomGen randomGen) => probabilityDistribution -> randomGen -> [sample] Source #

getMean :: Fractional mean => probabilityDistribution -> mean Source #

getStandardDeviation :: Floating standardDeviation => probabilityDistribution -> standardDeviation Source #

getVariance :: Floating variance => probabilityDistribution -> variance Source #

Instances

(RealFloat parameter, Show parameter, Random parameter) => Distribution (DiscreteDistribution parameter) Source #
Methods generatePopulation :: (Fractional sample, RandomGen randomGen) => DiscreteDistribution parameter -> randomGen -> [sample] Source # getMean :: Fractional mean => DiscreteDistribution parameter -> mean Source # getStandardDeviation :: Floating standardDeviation => DiscreteDistribution parameter -> standardDeviation Source # getVariance :: Floating variance => DiscreteDistribution parameter -> variance Source #
(RealFloat parameter, Show parameter, Random parameter) => Distribution (ContinuousDistribution parameter) Source #
Methods generatePopulation :: (Fractional sample, RandomGen randomGen) => ContinuousDistribution parameter -> randomGen -> [sample] Source # getMean :: Fractional mean => ContinuousDistribution parameter -> mean Source # getStandardDeviation :: Floating standardDeviation => ContinuousDistribution parameter -> standardDeviation Source # getVariance :: Floating variance => ContinuousDistribution parameter -> variance Source #

Types

Data-types

data ContinuousDistribution parameter Source #

Describes continuous probability-distributions; https://en.wikipedia.org/wiki/List_of_probability_distributions#Continuous_distributions.

Constructors

ExponentialDistribution parameter	Defines an Exponential-distribution with a particular lambda; https://en.wikipedia.org/wiki/Exponential_distribution.
LogNormalDistribution parameter parameter	Defines a distribution whose logarithm is normally distributed with a particular mean & variance; https://en.wikipedia.org/wiki/Lognormal.
NormalDistribution parameter parameter	Defines a Normal-distribution with a particular mean & variance; https://en.wikipedia.org/wiki/Normal_distribution.
UniformDistribution (Interval parameter)	Defines a Uniform-distribution within a closed interval; https://en.wikipedia.org/wiki/Uniform_distribution.

Instances

Eq parameter => Eq (ContinuousDistribution parameter) Source #
Methods (==) :: ContinuousDistribution parameter -> ContinuousDistribution parameter -> Bool # (/=) :: ContinuousDistribution parameter -> ContinuousDistribution parameter -> Bool #
Read parameter => Read (ContinuousDistribution parameter) Source #
Methods readsPrec :: Int -> ReadS (ContinuousDistribution parameter) # readList :: ReadS [ContinuousDistribution parameter] # readPrec :: ReadPrec (ContinuousDistribution parameter) # readListPrec :: ReadPrec [ContinuousDistribution parameter] #
Show parameter => Show (ContinuousDistribution parameter) Source #
Methods showsPrec :: Int -> ContinuousDistribution parameter -> ShowS # show :: ContinuousDistribution parameter -> String # showList :: [ContinuousDistribution parameter] -> ShowS #
(Floating parameter, Ord parameter, Show parameter) => SelfValidator (ContinuousDistribution parameter) Source #
Methods getErrors :: ContinuousDistribution parameter -> [String] # isValid :: ContinuousDistribution parameter -> Bool #
(RealFloat parameter, Show parameter, Random parameter) => Distribution (ContinuousDistribution parameter) Source #
Methods generatePopulation :: (Fractional sample, RandomGen randomGen) => ContinuousDistribution parameter -> randomGen -> [sample] Source # getMean :: Fractional mean => ContinuousDistribution parameter -> mean Source # getStandardDeviation :: Floating standardDeviation => ContinuousDistribution parameter -> standardDeviation Source # getVariance :: Floating variance => ContinuousDistribution parameter -> variance Source #

data DiscreteDistribution parameter Source #

Describes discrete probability-distributions; https://en.wikipedia.org/wiki/List_of_probability_distributions#Discrete_distributions.

Constructors

PoissonDistribution parameter	Defines an Poisson-distribution with a particular lambda; https://en.wikipedia.org/wiki/Poisson_distribution.
ShiftedGeometricDistribution parameter	Defines an Geometric-distribution with a particular probability of success; https://en.wikipedia.org/wiki/Geometric_distribution.

Instances

Eq parameter => Eq (DiscreteDistribution parameter) Source #
Methods (==) :: DiscreteDistribution parameter -> DiscreteDistribution parameter -> Bool # (/=) :: DiscreteDistribution parameter -> DiscreteDistribution parameter -> Bool #
Read parameter => Read (DiscreteDistribution parameter) Source #
Methods readsPrec :: Int -> ReadS (DiscreteDistribution parameter) # readList :: ReadS [DiscreteDistribution parameter] # readPrec :: ReadPrec (DiscreteDistribution parameter) # readListPrec :: ReadPrec [DiscreteDistribution parameter] #
Show parameter => Show (DiscreteDistribution parameter) Source #
Methods showsPrec :: Int -> DiscreteDistribution parameter -> ShowS # show :: DiscreteDistribution parameter -> String # showList :: [DiscreteDistribution parameter] -> ShowS #
(Num parameter, Ord parameter, Show parameter) => SelfValidator (DiscreteDistribution parameter) Source #
Methods getErrors :: DiscreteDistribution parameter -> [String] # isValid :: DiscreteDistribution parameter -> Bool #
(RealFloat parameter, Show parameter, Random parameter) => Distribution (DiscreteDistribution parameter) Source #
Methods generatePopulation :: (Fractional sample, RandomGen randomGen) => DiscreteDistribution parameter -> randomGen -> [sample] Source # getMean :: Fractional mean => DiscreteDistribution parameter -> mean Source # getStandardDeviation :: Floating standardDeviation => DiscreteDistribution parameter -> standardDeviation Source # getVariance :: Floating variance => DiscreteDistribution parameter -> variance Source #

Functions

maxPreciseInteger :: RealFloat a => a -> Integer Source #

The maximum integer which can be accurately represented as a Double.

boxMullerTransform Source #

Arguments

:: (Floating f, Ord f, Show f)
=> (f, f)	Independent, uniformly distributed random numbers, which must be within the semi-closed unit interval, (0,1].
-> (f, f)	Independent, normally distributed random numbers, with standardized mean=0 and variance=1.

Converts a pair of independent uniformly distributed random numbers, within the semi-closed unit interval (0,1], to a pair of independent normally distributed random numbers, of standardized mean=0, and variance=1.
https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform.

generateStandardizedNormalDistribution :: (RealFloat f, Show f, Random f, RandomGen randomGen) => randomGen -> [f] Source #

Uses the supplied random-number generator, to generate a conceptually infinite list, of normally distributed random numbers, with standardized mean=0, and variance=1.
https://en.wikipedia.org/wiki/Normal_distribution, http://mathworld.wolfram.com/NormalDistribution.html.

generateContinuousPopulation Source #

Arguments

:: (RealFloat f, Show f, Random f, RandomGen randomGen)
=> ContinuousDistribution f
-> randomGen	A generator of uniformly distributed random numbers.
-> [f]

Uses the supplied random-number generator, to generate a conceptually infinite population, with the specified continuous probability-distribution.

generateDiscretePopulation Source #

Arguments

:: (Integral sample, Ord parameter, RealFloat parameter, Show parameter, Random parameter, RandomGen randomGen)
=> DiscreteDistribution parameter
-> randomGen	A generator of uniformly distributed random numbers.
-> [sample]

Uses the supplied random-number generator, to generate a conceptually infinite population, with the specified discrete probability-distribution.