Safe Haskell	None
Language	Haskell98

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 Source

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 Source

Arguments

:: Fractional mean
=> probabilityDistribution
-> mean	The theoretical mean.

getStandardDeviation Source

Arguments

:: Floating standardDeviation
=> probabilityDistribution
-> standardDeviation	The theoretical standard-deviation.

getVariance Source

Arguments

:: Floating variance
=> probabilityDistribution
-> variance	The theoretical variance.

Instances

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

Types

Data-types

data ContinuousDistribution parameter Source

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

Constructors

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

Instances

Eq parameter => Eq (ContinuousDistribution parameter)
Read parameter => Read (ContinuousDistribution parameter)
Show parameter => Show (ContinuousDistribution parameter)
(Floating parameter, Ord parameter, Show parameter) => SelfValidator (ContinuousDistribution parameter)
(RealFloat parameter, Show parameter, Random parameter) => Distribution (ContinuousDistribution parameter)

data DiscreteDistribution parameter Source

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

Constructors

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

Instances

Eq parameter => Eq (DiscreteDistribution parameter)
Read parameter => Read (DiscreteDistribution parameter)
Show parameter => Show (DiscreteDistribution parameter)
(Num parameter, Ord parameter, Show parameter) => SelfValidator (DiscreteDistribution parameter)
(RealFloat parameter, Show parameter, Random parameter) => Distribution (DiscreteDistribution parameter)

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.
http://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.
http://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.