Data.Random.Distribution

Documentation

class Distribution d t where

A Distribution is a data representation of a random variable's probability structure. For example, in Data.Random.Distribution.Normal, the Normal distribution is defined as:

data Normal a
    = StdNormal
    | Normal a a

Where the two parameters of the Normal data constructor are the mean and standard deviation of the random variable, respectively. To make use of the Normal type, one can convert it to an rvar and manipulate it or sample it directly:

x <- sample (rvar (Normal 10 2))
x <- sample (Normal 10 2)

A Distribution is typically more transparent than an RVar but less composable (precisely because of that transparency). There are several practical uses for types implementing Distribution:

• Typically, a Distribution will expose several parameters of a standard mathematical model of a probability distribution, such as mean and std deviation for the normal distribution. Thus, they can be manipulated analytically using mathematical insights about the distributions they represent. For example, a collection of bernoulli variables could be simplified into a (hopefully) smaller collection of binomial variables.
• Because they are generally just containers for parameters, they can be easily serialized to persistent storage or read from user-supplied configurations (eg, initialization data for a simulation).
• If a type additionally implements the CDF subclass, which extends Distribution with a cumulative density function, an arbitrary random variable x can be tested against the distribution by testing fmap (cdf dist) x for uniformity.

On the other hand, most Distributions will not be closed under all the same operations as RVar (which, being a monad, has a fully turing-complete internal computational model). The sum of two uniformly-distributed variables, for example, is not uniformly distributed. To support general composition, the Distribution class defines a function rvar to construct the more-abstract and more-composable RVar representation of a random variable.

Minimal complete definition

Nothing

Methods

rvar :: d t -> RVar t

Return a random variable with this distribution.

rvarT :: d t -> RVarT n t

Return a random variable with the given distribution, pre-lifted to an arbitrary RVarT. Any arbitrary RVar can also be converted to an 'RVarT m' for an arbitrary m, using either lift or sample.

Instances

Distribution StdUniform Bool

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform Bool -> RVar Bool

rvarT :: StdUniform Bool -> RVarT n Bool

Distribution StdUniform Char

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform Char -> RVar Char

rvarT :: StdUniform Char -> RVarT n Char

Distribution StdUniform Double

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform Double -> RVar Double

rvarT :: StdUniform Double -> RVarT n Double

Distribution StdUniform Float

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform Float -> RVar Float

rvarT :: StdUniform Float -> RVarT n Float

Distribution StdUniform Int

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform Int -> RVar Int

rvarT :: StdUniform Int -> RVarT n Int

Distribution StdUniform Int8

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform Int8 -> RVar Int8

rvarT :: StdUniform Int8 -> RVarT n Int8

Distribution StdUniform Int16

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform Int16 -> RVar Int16

rvarT :: StdUniform Int16 -> RVarT n Int16

Distribution StdUniform Int32

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform Int32 -> RVar Int32

rvarT :: StdUniform Int32 -> RVarT n Int32

Distribution StdUniform Int64

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform Int64 -> RVar Int64

rvarT :: StdUniform Int64 -> RVarT n Int64

Distribution StdUniform Ordering

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform Ordering -> RVar Ordering

rvarT :: StdUniform Ordering -> RVarT n Ordering

Distribution StdUniform Word

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform Word -> RVar Word

rvarT :: StdUniform Word -> RVarT n Word

Distribution StdUniform Word8

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform Word8 -> RVar Word8

rvarT :: StdUniform Word8 -> RVarT n Word8

Distribution StdUniform Word16

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform Word16 -> RVar Word16

rvarT :: StdUniform Word16 -> RVarT n Word16

Distribution StdUniform Word32

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform Word32 -> RVar Word32

rvarT :: StdUniform Word32 -> RVarT n Word32

Distribution StdUniform Word64

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform Word64 -> RVar Word64

rvarT :: StdUniform Word64 -> RVarT n Word64

Distribution StdUniform ()

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform () -> RVar ()

rvarT :: StdUniform () -> RVarT n ()

Distribution Uniform Bool

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Bool -> RVar Bool

rvarT :: Uniform Bool -> RVarT n Bool

Distribution Uniform Char

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Char -> RVar Char

rvarT :: Uniform Char -> RVarT n Char

Distribution Uniform Double

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Double -> RVar Double

rvarT :: Uniform Double -> RVarT n Double

Distribution Uniform Float

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Float -> RVar Float

rvarT :: Uniform Float -> RVarT n Float

Distribution Uniform Int

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Int -> RVar Int

rvarT :: Uniform Int -> RVarT n Int

Distribution Uniform Int8

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Int8 -> RVar Int8

rvarT :: Uniform Int8 -> RVarT n Int8

Distribution Uniform Int16

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Int16 -> RVar Int16

rvarT :: Uniform Int16 -> RVarT n Int16

Distribution Uniform Int32

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Int32 -> RVar Int32

rvarT :: Uniform Int32 -> RVarT n Int32

Distribution Uniform Int64

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Int64 -> RVar Int64

rvarT :: Uniform Int64 -> RVarT n Int64

Distribution Uniform Integer

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Integer -> RVar Integer

rvarT :: Uniform Integer -> RVarT n Integer

Distribution Uniform Ordering

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Ordering -> RVar Ordering

rvarT :: Uniform Ordering -> RVarT n Ordering

Distribution Uniform Word

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Word -> RVar Word

rvarT :: Uniform Word -> RVarT n Word

Distribution Uniform Word8

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Word8 -> RVar Word8

rvarT :: Uniform Word8 -> RVarT n Word8

Distribution Uniform Word16

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Word16 -> RVar Word16

rvarT :: Uniform Word16 -> RVarT n Word16

Distribution Uniform Word32

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Word32 -> RVar Word32

rvarT :: Uniform Word32 -> RVarT n Word32

Distribution Uniform Word64

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform Word64 -> RVar Word64

rvarT :: Uniform Word64 -> RVarT n Word64

Distribution Uniform ()

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform () -> RVar ()

rvarT :: Uniform () -> RVarT n ()

(Floating a, Distribution StdUniform a) => Distribution Weibull a

Defined in Data.Random.Distribution.Weibull

Methods

rvar :: Weibull a -> RVar a

rvarT :: Weibull a -> RVarT n a

(RealFloat a, Ord a, Distribution StdUniform a) => Distribution Triangular a

Defined in Data.Random.Distribution.Triangular

Methods

rvar :: Triangular a -> RVar a

rvarT :: Triangular a -> RVarT n a

(Floating a, Distribution StdUniform a) => Distribution StretchedExponential a

Defined in Data.Random.Distribution.StretchedExponential

Methods

rvar :: StretchedExponential a -> RVar a

rvarT :: StretchedExponential a -> RVarT n a

(RealFloat a, Distribution StdUniform a) => Distribution Rayleigh a

Defined in Data.Random.Distribution.Rayleigh

Methods

rvar :: Rayleigh a -> RVar a

rvarT :: Rayleigh a -> RVarT n a

Distribution Normal Double

Defined in Data.Random.Distribution.Normal

Methods

rvar :: Normal Double -> RVar Double

rvarT :: Normal Double -> RVarT n Double

Distribution Normal Float

Defined in Data.Random.Distribution.Normal

Methods

rvar :: Normal Float -> RVar Float

rvarT :: Normal Float -> RVarT n Float

(Floating a, Ord a, Distribution Normal a, Distribution StdUniform a) => Distribution Gamma a

Defined in Data.Random.Distribution.Gamma

Methods

rvar :: Gamma a -> RVar a

rvarT :: Gamma a -> RVarT n a

(Floating a, Distribution StdUniform a) => Distribution Exponential a

Defined in Data.Random.Distribution.Exponential

Methods

rvar :: Exponential a -> RVar a

rvarT :: Exponential a -> RVarT n a

(Fractional t, Distribution Gamma t) => Distribution ChiSquare t

Defined in Data.Random.Distribution.ChiSquare

Methods

rvar :: ChiSquare t -> RVar t

rvarT :: ChiSquare t -> RVarT n t

(Floating a, Distribution Normal a, Distribution ChiSquare a) => Distribution T a

Defined in Data.Random.Distribution.T

Methods

rvar :: T a -> RVar a

rvarT :: T a -> RVarT n a

Distribution Beta Double

Defined in Data.Random.Distribution.Beta

Methods

rvar :: Beta Double -> RVar Double

rvarT :: Beta Double -> RVarT n Double

Distribution Beta Float

Defined in Data.Random.Distribution.Beta

Methods

rvar :: Beta Float -> RVar Float

rvarT :: Beta Float -> RVarT n Float

(Floating a, Distribution StdUniform a) => Distribution Pareto a

Defined in Data.Random.Distribution.Pareto

Methods

rvar :: Pareto a -> RVar a

rvarT :: Pareto a -> RVarT n a

HasResolution r => Distribution StdUniform (Fixed r)

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform (Fixed r) -> RVar (Fixed r)

rvarT :: StdUniform (Fixed r) -> RVarT n (Fixed r)

HasResolution r => Distribution Uniform (Fixed r)

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform (Fixed r) -> RVar (Fixed r)

rvarT :: Uniform (Fixed r) -> RVarT n (Fixed r)

(Ord a, Fractional a, Distribution StdUniform a) => Distribution StdSimplex [a]

Defined in Data.Random.Distribution.Simplex

Methods

rvar :: StdSimplex [a] -> RVar [a]

rvarT :: StdSimplex [a] -> RVarT n [a]

(Fractional a, Distribution Gamma a) => Distribution Dirichlet [a]

Defined in Data.Random.Distribution.Dirichlet

Methods

rvar :: Dirichlet [a] -> RVar [a]

rvarT :: Dirichlet [a] -> RVarT n [a]

(Num t, Ord t, Vector v t) => Distribution (Ziggurat v) t

Defined in Data.Random.Distribution.Ziggurat

Methods

rvar :: Ziggurat v t -> RVar t

rvarT :: Ziggurat v t -> RVarT n t

(Integral a, Floating b, Ord b, Distribution Normal b, Distribution StdUniform b) => Distribution (Erlang a) b

Defined in Data.Random.Distribution.Gamma

Methods

rvar :: Erlang a b -> RVar b

rvarT :: Erlang a b -> RVarT n b

(Fractional p, Ord p, Distribution Uniform p) => Distribution (Categorical p) a

Defined in Data.Random.Distribution.Categorical

Methods

rvar :: Categorical p a -> RVar a

rvarT :: Categorical p a -> RVarT n a

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Integer

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Integer -> RVar Integer

rvarT :: Binomial b Integer -> RVarT n Integer

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Int

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Int -> RVar Int

rvarT :: Binomial b Int -> RVarT n Int

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Int8

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Int8 -> RVar Int8

rvarT :: Binomial b Int8 -> RVarT n Int8

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Int16

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Int16 -> RVar Int16

rvarT :: Binomial b Int16 -> RVarT n Int16

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Int32

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Int32 -> RVar Int32

rvarT :: Binomial b Int32 -> RVarT n Int32

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Int64

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Int64 -> RVar Int64

rvarT :: Binomial b Int64 -> RVarT n Int64

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Word -> RVar Word

rvarT :: Binomial b Word -> RVarT n Word

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word8

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Word8 -> RVar Word8

rvarT :: Binomial b Word8 -> RVarT n Word8

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word16

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Word16 -> RVar Word16

rvarT :: Binomial b Word16 -> RVarT n Word16

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word32

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Word32 -> RVar Word32

rvarT :: Binomial b Word32 -> RVarT n Word32

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word64

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Word64 -> RVar Word64

rvarT :: Binomial b Word64 -> RVarT n Word64

Distribution (Binomial b) Integer => Distribution (Binomial b) Float

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Float -> RVar Float

rvarT :: Binomial b Float -> RVarT n Float

Distribution (Binomial b) Integer => Distribution (Binomial b) Double

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Double -> RVar Double

rvarT :: Binomial b Double -> RVarT n Double

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Integer) b, Distribution (Binomial b) Integer) => Distribution (Poisson b) Integer

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Integer -> RVar Integer

rvarT :: Poisson b Integer -> RVarT n Integer

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Int) b, Distribution (Binomial b) Int) => Distribution (Poisson b) Int

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Int -> RVar Int

rvarT :: Poisson b Int -> RVarT n Int

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Int8) b, Distribution (Binomial b) Int8) => Distribution (Poisson b) Int8

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Int8 -> RVar Int8

rvarT :: Poisson b Int8 -> RVarT n Int8

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Int16) b, Distribution (Binomial b) Int16) => Distribution (Poisson b) Int16

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Int16 -> RVar Int16

rvarT :: Poisson b Int16 -> RVarT n Int16

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Int32) b, Distribution (Binomial b) Int32) => Distribution (Poisson b) Int32

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Int32 -> RVar Int32

rvarT :: Poisson b Int32 -> RVarT n Int32

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Int64) b, Distribution (Binomial b) Int64) => Distribution (Poisson b) Int64

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Int64 -> RVar Int64

rvarT :: Poisson b Int64 -> RVarT n Int64

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Word) b, Distribution (Binomial b) Word) => Distribution (Poisson b) Word

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Word -> RVar Word

rvarT :: Poisson b Word -> RVarT n Word

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Word8) b, Distribution (Binomial b) Word8) => Distribution (Poisson b) Word8

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Word8 -> RVar Word8

rvarT :: Poisson b Word8 -> RVarT n Word8

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Word16) b, Distribution (Binomial b) Word16) => Distribution (Poisson b) Word16

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Word16 -> RVar Word16

rvarT :: Poisson b Word16 -> RVarT n Word16

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Word32) b, Distribution (Binomial b) Word32) => Distribution (Poisson b) Word32

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Word32 -> RVar Word32

rvarT :: Poisson b Word32 -> RVarT n Word32

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Word64) b, Distribution (Binomial b) Word64) => Distribution (Poisson b) Word64

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Word64 -> RVar Word64

rvarT :: Poisson b Word64 -> RVarT n Word64

Distribution (Poisson b) Integer => Distribution (Poisson b) Float

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Float -> RVar Float

rvarT :: Poisson b Float -> RVarT n Float

Distribution (Poisson b) Integer => Distribution (Poisson b) Double

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Double -> RVar Double

rvarT :: Poisson b Double -> RVarT n Double

(Fractional b, Ord b, Distribution StdUniform b) => Distribution (Bernoulli b) Bool

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b Bool -> RVar Bool

rvarT :: Bernoulli b Bool -> RVarT n Bool

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Integer

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b Integer -> RVar Integer

rvarT :: Bernoulli b Integer -> RVarT n Integer

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Int

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b Int -> RVar Int

rvarT :: Bernoulli b Int -> RVarT n Int

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Int8

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b Int8 -> RVar Int8

rvarT :: Bernoulli b Int8 -> RVarT n Int8

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Int16

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b Int16 -> RVar Int16

rvarT :: Bernoulli b Int16 -> RVarT n Int16

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Int32

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b Int32 -> RVar Int32

rvarT :: Bernoulli b Int32 -> RVarT n Int32

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Int64

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b Int64 -> RVar Int64

rvarT :: Bernoulli b Int64 -> RVarT n Int64

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Word

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b Word -> RVar Word

rvarT :: Bernoulli b Word -> RVarT n Word

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Word8

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b Word8 -> RVar Word8

rvarT :: Bernoulli b Word8 -> RVarT n Word8

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Word16

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b Word16 -> RVar Word16

rvarT :: Bernoulli b Word16 -> RVarT n Word16

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Word32

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b Word32 -> RVar Word32

rvarT :: Bernoulli b Word32 -> RVarT n Word32

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Word64

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b Word64 -> RVar Word64

rvarT :: Bernoulli b Word64 -> RVarT n Word64

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Float

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b Float -> RVar Float

rvarT :: Bernoulli b Float -> RVarT n Float

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Double

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b Double -> RVar Double

rvarT :: Bernoulli b Double -> RVarT n Double

(Num a, Eq a, Fractional p, Distribution (Binomial p) a) => Distribution (Multinomial p) [a]

Defined in Data.Random.Distribution.Multinomial

Methods

rvar :: Multinomial p [a] -> RVar [a]

rvarT :: Multinomial p [a] -> RVarT n [a]

(Distribution (Bernoulli b) Bool, RealFloat a) => Distribution (Bernoulli b) (Complex a)

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b (Complex a) -> RVar (Complex a)

rvarT :: Bernoulli b (Complex a) -> RVarT n (Complex a)

(Distribution (Bernoulli b) Bool, Integral a) => Distribution (Bernoulli b) (Ratio a)

Defined in Data.Random.Distribution.Bernoulli

Methods

rvar :: Bernoulli b (Ratio a) -> RVar (Ratio a)

rvarT :: Bernoulli b (Ratio a) -> RVarT n (Ratio a)

class Distribution d t => PDF d t where

Minimal complete definition

Nothing

Methods

pdf :: d t -> t -> Double

logPdf :: d t -> t -> Double

Instances

PDF StdUniform Double

Defined in Data.Random.Distribution.Uniform

Methods

pdf :: StdUniform Double -> Double -> Double

logPdf :: StdUniform Double -> Double -> Double

PDF StdUniform Float

Defined in Data.Random.Distribution.Uniform

Methods

pdf :: StdUniform Float -> Float -> Double

logPdf :: StdUniform Float -> Float -> Double

(Real a, Floating a, Distribution Normal a) => PDF Normal a

Defined in Data.Random.Distribution.Normal

Methods

pdf :: Normal a -> a -> Double

logPdf :: Normal a -> a -> Double

PDF Beta Double

Defined in Data.Random.Distribution.Beta

Methods

pdf :: Beta Double -> Double -> Double

logPdf :: Beta Double -> Double -> Double

PDF Beta Float

Defined in Data.Random.Distribution.Beta

Methods

pdf :: Beta Float -> Float -> Double

logPdf :: Beta Float -> Float -> Double

(Real b, Distribution (Binomial b) Integer) => PDF (Binomial b) Integer

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Integer -> Integer -> Double

logPdf :: Binomial b Integer -> Integer -> Double

(Real b, Distribution (Binomial b) Int) => PDF (Binomial b) Int

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Int -> Int -> Double

logPdf :: Binomial b Int -> Int -> Double

(Real b, Distribution (Binomial b) Int8) => PDF (Binomial b) Int8

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Int8 -> Int8 -> Double

logPdf :: Binomial b Int8 -> Int8 -> Double

(Real b, Distribution (Binomial b) Int16) => PDF (Binomial b) Int16

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Int16 -> Int16 -> Double

logPdf :: Binomial b Int16 -> Int16 -> Double

(Real b, Distribution (Binomial b) Int32) => PDF (Binomial b) Int32

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Int32 -> Int32 -> Double

logPdf :: Binomial b Int32 -> Int32 -> Double

(Real b, Distribution (Binomial b) Int64) => PDF (Binomial b) Int64

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Int64 -> Int64 -> Double

logPdf :: Binomial b Int64 -> Int64 -> Double

(Real b, Distribution (Binomial b) Word) => PDF (Binomial b) Word

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Word -> Word -> Double

logPdf :: Binomial b Word -> Word -> Double

(Real b, Distribution (Binomial b) Word8) => PDF (Binomial b) Word8

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Word8 -> Word8 -> Double

logPdf :: Binomial b Word8 -> Word8 -> Double

(Real b, Distribution (Binomial b) Word16) => PDF (Binomial b) Word16

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Word16 -> Word16 -> Double

logPdf :: Binomial b Word16 -> Word16 -> Double

(Real b, Distribution (Binomial b) Word32) => PDF (Binomial b) Word32

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Word32 -> Word32 -> Double

logPdf :: Binomial b Word32 -> Word32 -> Double

(Real b, Distribution (Binomial b) Word64) => PDF (Binomial b) Word64

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Word64 -> Word64 -> Double

logPdf :: Binomial b Word64 -> Word64 -> Double

PDF (Binomial b) Integer => PDF (Binomial b) Float

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Float -> Float -> Double

logPdf :: Binomial b Float -> Float -> Double

PDF (Binomial b) Integer => PDF (Binomial b) Double

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Double -> Double -> Double

logPdf :: Binomial b Double -> Double -> Double

(Real b, Distribution (Poisson b) Integer) => PDF (Poisson b) Integer

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Integer -> Integer -> Double

logPdf :: Poisson b Integer -> Integer -> Double

(Real b, Distribution (Poisson b) Int) => PDF (Poisson b) Int

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Int -> Int -> Double

logPdf :: Poisson b Int -> Int -> Double

(Real b, Distribution (Poisson b) Int8) => PDF (Poisson b) Int8

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Int8 -> Int8 -> Double

logPdf :: Poisson b Int8 -> Int8 -> Double

(Real b, Distribution (Poisson b) Int16) => PDF (Poisson b) Int16

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Int16 -> Int16 -> Double

logPdf :: Poisson b Int16 -> Int16 -> Double

(Real b, Distribution (Poisson b) Int32) => PDF (Poisson b) Int32

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Int32 -> Int32 -> Double

logPdf :: Poisson b Int32 -> Int32 -> Double

(Real b, Distribution (Poisson b) Int64) => PDF (Poisson b) Int64

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Int64 -> Int64 -> Double

logPdf :: Poisson b Int64 -> Int64 -> Double

(Real b, Distribution (Poisson b) Word) => PDF (Poisson b) Word

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Word -> Word -> Double

logPdf :: Poisson b Word -> Word -> Double

(Real b, Distribution (Poisson b) Word8) => PDF (Poisson b) Word8

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Word8 -> Word8 -> Double

logPdf :: Poisson b Word8 -> Word8 -> Double

(Real b, Distribution (Poisson b) Word16) => PDF (Poisson b) Word16

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Word16 -> Word16 -> Double

logPdf :: Poisson b Word16 -> Word16 -> Double

(Real b, Distribution (Poisson b) Word32) => PDF (Poisson b) Word32

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Word32 -> Word32 -> Double

logPdf :: Poisson b Word32 -> Word32 -> Double

(Real b, Distribution (Poisson b) Word64) => PDF (Poisson b) Word64

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Word64 -> Word64 -> Double

logPdf :: Poisson b Word64 -> Word64 -> Double

PDF (Poisson b) Integer => PDF (Poisson b) Float

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Float -> Float -> Double

logPdf :: Poisson b Float -> Float -> Double

PDF (Poisson b) Integer => PDF (Poisson b) Double

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Double -> Double -> Double

logPdf :: Poisson b Double -> Double -> Double

class Distribution d t => CDF d t where

Methods

cdf :: d t -> t -> Double

Return the cumulative distribution function of this distribution. That is, a function taking x :: t to the probability that the next sample will return a value less than or equal to x, according to some order or partial order (not necessarily an obvious one).

In the case where t is an instance of Ord, cdf should correspond to the CDF with respect to that order.

In other cases, cdf is only required to satisfy the following law: fmap (cdf d) (rvar d) must be uniformly distributed over (0,1). Inclusion of either endpoint is optional, though the preferred range is (0,1].

Note that this definition requires that cdf for a product type should _not_ be a joint CDF as commonly defined, as that definition violates both conditions. Instead, it should be a univariate CDF over the product type. That is, it should represent the CDF with respect to the lexicographic order of the product.

The present specification is probably only really useful for testing conformance of a variable to its target distribution, and I am open to suggestions for more-useful specifications (especially with regard to the interaction with product types).

Instances

CDF StdUniform Bool

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Bool -> Bool -> Double

CDF StdUniform Char

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Char -> Char -> Double

CDF StdUniform Double

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Double -> Double -> Double

CDF StdUniform Float

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Float -> Float -> Double

CDF StdUniform Int

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Int -> Int -> Double

CDF StdUniform Int8

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Int8 -> Int8 -> Double

CDF StdUniform Int16

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Int16 -> Int16 -> Double

CDF StdUniform Int32

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Int32 -> Int32 -> Double

CDF StdUniform Int64

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Int64 -> Int64 -> Double

CDF StdUniform Ordering

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Ordering -> Ordering -> Double

CDF StdUniform Word

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Word -> Word -> Double

CDF StdUniform Word8

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Word8 -> Word8 -> Double

CDF StdUniform Word16

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Word16 -> Word16 -> Double

CDF StdUniform Word32

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Word32 -> Word32 -> Double

CDF StdUniform Word64

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Word64 -> Word64 -> Double

CDF StdUniform ()

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform () -> () -> Double

CDF Uniform Bool

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Bool -> Bool -> Double

CDF Uniform Char

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Char -> Char -> Double

CDF Uniform Double

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Double -> Double -> Double

CDF Uniform Float

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Float -> Float -> Double

CDF Uniform Int

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Int -> Int -> Double

CDF Uniform Int8

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Int8 -> Int8 -> Double

CDF Uniform Int16

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Int16 -> Int16 -> Double

CDF Uniform Int32

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Int32 -> Int32 -> Double

CDF Uniform Int64

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Int64 -> Int64 -> Double

CDF Uniform Integer

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Integer -> Integer -> Double

CDF Uniform Ordering

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Ordering -> Ordering -> Double

CDF Uniform Word

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Word -> Word -> Double

CDF Uniform Word8

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Word8 -> Word8 -> Double

CDF Uniform Word16

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Word16 -> Word16 -> Double

CDF Uniform Word32

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Word32 -> Word32 -> Double

CDF Uniform Word64

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Word64 -> Word64 -> Double

CDF Uniform ()

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform () -> () -> Double

(Real a, Distribution Weibull a) => CDF Weibull a

Defined in Data.Random.Distribution.Weibull

Methods

cdf :: Weibull a -> a -> Double

(RealFrac a, Distribution Triangular a) => CDF Triangular a

Defined in Data.Random.Distribution.Triangular

Methods

cdf :: Triangular a -> a -> Double

(Real a, Distribution StretchedExponential a) => CDF StretchedExponential a

Defined in Data.Random.Distribution.StretchedExponential

Methods

cdf :: StretchedExponential a -> a -> Double

(Real a, Distribution Rayleigh a) => CDF Rayleigh a

Defined in Data.Random.Distribution.Rayleigh

Methods

cdf :: Rayleigh a -> a -> Double

(Real a, Distribution Normal a) => CDF Normal a

Defined in Data.Random.Distribution.Normal

Methods

cdf :: Normal a -> a -> Double

(Real a, Distribution Gamma a) => CDF Gamma a

Defined in Data.Random.Distribution.Gamma

Methods

cdf :: Gamma a -> a -> Double

(Real a, Distribution Exponential a) => CDF Exponential a

Defined in Data.Random.Distribution.Exponential

Methods

cdf :: Exponential a -> a -> Double

(Real t, Distribution ChiSquare t) => CDF ChiSquare t

Defined in Data.Random.Distribution.ChiSquare

Methods

cdf :: ChiSquare t -> t -> Double

(Real a, Distribution T a) => CDF T a

Defined in Data.Random.Distribution.T

Methods

cdf :: T a -> a -> Double

(Real a, Distribution Pareto a) => CDF Pareto a

Defined in Data.Random.Distribution.Pareto

Methods

cdf :: Pareto a -> a -> Double

HasResolution r => CDF StdUniform (Fixed r)

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform (Fixed r) -> Fixed r -> Double

HasResolution r => CDF Uniform (Fixed r)

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform (Fixed r) -> Fixed r -> Double

(Integral a, Real b, Distribution (Erlang a) b) => CDF (Erlang a) b

Defined in Data.Random.Distribution.Gamma

Methods

cdf :: Erlang a b -> b -> Double

(Real b, Distribution (Binomial b) Integer) => CDF (Binomial b) Integer

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Integer -> Integer -> Double

(Real b, Distribution (Binomial b) Int) => CDF (Binomial b) Int

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Int -> Int -> Double

(Real b, Distribution (Binomial b) Int8) => CDF (Binomial b) Int8

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Int8 -> Int8 -> Double

(Real b, Distribution (Binomial b) Int16) => CDF (Binomial b) Int16

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Int16 -> Int16 -> Double

(Real b, Distribution (Binomial b) Int32) => CDF (Binomial b) Int32

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Int32 -> Int32 -> Double

(Real b, Distribution (Binomial b) Int64) => CDF (Binomial b) Int64

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Int64 -> Int64 -> Double

(Real b, Distribution (Binomial b) Word) => CDF (Binomial b) Word

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Word -> Word -> Double

(Real b, Distribution (Binomial b) Word8) => CDF (Binomial b) Word8

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Word8 -> Word8 -> Double

(Real b, Distribution (Binomial b) Word16) => CDF (Binomial b) Word16

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Word16 -> Word16 -> Double

(Real b, Distribution (Binomial b) Word32) => CDF (Binomial b) Word32

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Word32 -> Word32 -> Double

(Real b, Distribution (Binomial b) Word64) => CDF (Binomial b) Word64

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Word64 -> Word64 -> Double

CDF (Binomial b) Integer => CDF (Binomial b) Float

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Float -> Float -> Double

CDF (Binomial b) Integer => CDF (Binomial b) Double

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Double -> Double -> Double

(Real b, Distribution (Poisson b) Integer) => CDF (Poisson b) Integer

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Integer -> Integer -> Double

(Real b, Distribution (Poisson b) Int) => CDF (Poisson b) Int

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Int -> Int -> Double

(Real b, Distribution (Poisson b) Int8) => CDF (Poisson b) Int8

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Int8 -> Int8 -> Double

(Real b, Distribution (Poisson b) Int16) => CDF (Poisson b) Int16

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Int16 -> Int16 -> Double

(Real b, Distribution (Poisson b) Int32) => CDF (Poisson b) Int32

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Int32 -> Int32 -> Double

(Real b, Distribution (Poisson b) Int64) => CDF (Poisson b) Int64

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Int64 -> Int64 -> Double

(Real b, Distribution (Poisson b) Word) => CDF (Poisson b) Word

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Word -> Word -> Double

(Real b, Distribution (Poisson b) Word8) => CDF (Poisson b) Word8

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Word8 -> Word8 -> Double

(Real b, Distribution (Poisson b) Word16) => CDF (Poisson b) Word16

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Word16 -> Word16 -> Double

(Real b, Distribution (Poisson b) Word32) => CDF (Poisson b) Word32

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Word32 -> Word32 -> Double

(Real b, Distribution (Poisson b) Word64) => CDF (Poisson b) Word64

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Word64 -> Word64 -> Double

CDF (Poisson b) Integer => CDF (Poisson b) Float

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Float -> Float -> Double

CDF (Poisson b) Integer => CDF (Poisson b) Double

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Double -> Double -> Double

(Distribution (Bernoulli b) Bool, Real b) => CDF (Bernoulli b) Bool

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b Bool -> Bool -> Double

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Integer

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b Integer -> Integer -> Double

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Int

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b Int -> Int -> Double

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Int8

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b Int8 -> Int8 -> Double

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Int16

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b Int16 -> Int16 -> Double

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Int32

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b Int32 -> Int32 -> Double

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Int64

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b Int64 -> Int64 -> Double

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Word

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b Word -> Word -> Double

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Word8

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b Word8 -> Word8 -> Double

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Word16

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b Word16 -> Word16 -> Double

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Word32

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b Word32 -> Word32 -> Double

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Word64

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b Word64 -> Word64 -> Double

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Float

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b Float -> Float -> Double

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Double

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b Double -> Double -> Double

(CDF (Bernoulli b) Bool, RealFloat a) => CDF (Bernoulli b) (Complex a)

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b (Complex a) -> Complex a -> Double

(CDF (Bernoulli b) Bool, Integral a) => CDF (Bernoulli b) (Ratio a)

Defined in Data.Random.Distribution.Bernoulli

Methods

cdf :: Bernoulli b (Ratio a) -> Ratio a -> Double