Factory.Math.Probability

AUTHOR

Dr. Alistair Ward

DESCRIPTION

Functions for probability-distributions.

CAVEAT

Because data-constructors are exposed, isValid need not be called.

Type-classes

class Distribution probabilityDistribution where

Defines a common interface for probability-distributions.

Minimal complete definition

generatePopulation, getMean

Methods

generatePopulation

Arguments

:: (Fractional sample, RandomGen randomGen)

=> probabilityDistribution

-> randomGen

A generator of uniformly distributed random numbers.

-> [sample]

CAVEAT: the integers generated for discrete distributions are represented by a fractional type; use generateDiscretePopulation if this is a problem.

getMean

Arguments

:: Fractional mean

=> probabilityDistribution

-> mean

The theoretical mean.

getStandardDeviation

Arguments

:: Floating standardDeviation

=> probabilityDistribution

-> standardDeviation

The theoretical standard-deviation.

getVariance

Arguments

:: Floating variance

=> probabilityDistribution

-> variance

The theoretical variance.

Instances

(RealFloat parameter, Show parameter, Random parameter) => Distribution (DiscreteDistribution parameter)

Defined in Factory.Math.Probability

Methods

generatePopulation :: (Fractional sample, RandomGen randomGen) => DiscreteDistribution parameter -> randomGen -> [sample]

getMean :: Fractional mean => DiscreteDistribution parameter -> mean

getStandardDeviation :: Floating standardDeviation => DiscreteDistribution parameter -> standardDeviation

getVariance :: Floating variance => DiscreteDistribution parameter -> variance

(RealFloat parameter, Show parameter, Random parameter) => Distribution (ContinuousDistribution parameter)

Defined in Factory.Math.Probability

Methods

generatePopulation :: (Fractional sample, RandomGen randomGen) => ContinuousDistribution parameter -> randomGen -> [sample]

getMean :: Fractional mean => ContinuousDistribution parameter -> mean

getStandardDeviation :: Floating standardDeviation => ContinuousDistribution parameter -> standardDeviation

getVariance :: Floating variance => ContinuousDistribution parameter -> variance

Types

Data-types

data ContinuousDistribution parameter

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)

Defined in Factory.Math.Probability

Methods

(==) :: ContinuousDistribution parameter -> ContinuousDistribution parameter -> Bool

(/=) :: ContinuousDistribution parameter -> ContinuousDistribution parameter -> Bool

Read parameter => Read (ContinuousDistribution parameter)

Defined in Factory.Math.Probability

Methods

readsPrec :: Int -> ReadS (ContinuousDistribution parameter)

readList :: ReadS [ContinuousDistribution parameter]

readPrec :: ReadPrec (ContinuousDistribution parameter)

readListPrec :: ReadPrec [ContinuousDistribution parameter]

Show parameter => Show (ContinuousDistribution parameter)

Defined in Factory.Math.Probability

Methods

showsPrec :: Int -> ContinuousDistribution parameter -> ShowS

show :: ContinuousDistribution parameter -> String

showList :: [ContinuousDistribution parameter] -> ShowS

(Floating parameter, Ord parameter, Show parameter) => SelfValidator (ContinuousDistribution parameter)

Defined in Factory.Math.Probability

Methods

getErrors :: ContinuousDistribution parameter -> [String]

isValid :: ContinuousDistribution parameter -> Bool

(RealFloat parameter, Show parameter, Random parameter) => Distribution (ContinuousDistribution parameter)

Defined in Factory.Math.Probability

Methods

generatePopulation :: (Fractional sample, RandomGen randomGen) => ContinuousDistribution parameter -> randomGen -> [sample]

getMean :: Fractional mean => ContinuousDistribution parameter -> mean

getStandardDeviation :: Floating standardDeviation => ContinuousDistribution parameter -> standardDeviation

getVariance :: Floating variance => ContinuousDistribution parameter -> variance

data DiscreteDistribution parameter

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)

Defined in Factory.Math.Probability

Methods

(==) :: DiscreteDistribution parameter -> DiscreteDistribution parameter -> Bool

(/=) :: DiscreteDistribution parameter -> DiscreteDistribution parameter -> Bool

Read parameter => Read (DiscreteDistribution parameter)

Defined in Factory.Math.Probability

Methods

readsPrec :: Int -> ReadS (DiscreteDistribution parameter)

readList :: ReadS [DiscreteDistribution parameter]

readPrec :: ReadPrec (DiscreteDistribution parameter)

readListPrec :: ReadPrec [DiscreteDistribution parameter]

Show parameter => Show (DiscreteDistribution parameter)

Defined in Factory.Math.Probability

Methods

showsPrec :: Int -> DiscreteDistribution parameter -> ShowS

show :: DiscreteDistribution parameter -> String

showList :: [DiscreteDistribution parameter] -> ShowS

(Num parameter, Ord parameter, Show parameter) => SelfValidator (DiscreteDistribution parameter)

Defined in Factory.Math.Probability

Methods

getErrors :: DiscreteDistribution parameter -> [String]

isValid :: DiscreteDistribution parameter -> Bool

(RealFloat parameter, Show parameter, Random parameter) => Distribution (DiscreteDistribution parameter)

Defined in Factory.Math.Probability

Methods

generatePopulation :: (Fractional sample, RandomGen randomGen) => DiscreteDistribution parameter -> randomGen -> [sample]

getMean :: Fractional mean => DiscreteDistribution parameter -> mean

getStandardDeviation :: Floating standardDeviation => DiscreteDistribution parameter -> standardDeviation

getVariance :: Floating variance => DiscreteDistribution parameter -> variance

Functions

maxPreciseInteger :: RealFloat a => a -> Integer

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

boxMullerTransform

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]

• 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, https://mathworld.wolfram.com/NormalDistribution.html.

generateContinuousPopulation

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

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.