Safe Haskell	None
Language	Haskell98

Data.Random.Distribution

Synopsis

Documentation

class Distribution d t where Source #

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.

Methods

rvar :: d t -> RVar t Source #

Return a random variable with this distribution.

rvarT :: d t -> RVarT n t Source #

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 Source #
Methods rvar :: StdUniform Bool -> RVar Bool Source # rvarT :: StdUniform Bool -> RVarT n Bool Source #
Distribution StdUniform Char Source #
Methods rvar :: StdUniform Char -> RVar Char Source # rvarT :: StdUniform Char -> RVarT n Char Source #
Distribution StdUniform Double Source #
Methods rvar :: StdUniform Double -> RVar Double Source # rvarT :: StdUniform Double -> RVarT n Double Source #
Distribution StdUniform Float Source #
Methods rvar :: StdUniform Float -> RVar Float Source # rvarT :: StdUniform Float -> RVarT n Float Source #
Distribution StdUniform Int Source #
Methods rvar :: StdUniform Int -> RVar Int Source # rvarT :: StdUniform Int -> RVarT n Int Source #
Distribution StdUniform Int8 Source #
Methods rvar :: StdUniform Int8 -> RVar Int8 Source # rvarT :: StdUniform Int8 -> RVarT n Int8 Source #
Distribution StdUniform Int16 Source #
Methods rvar :: StdUniform Int16 -> RVar Int16 Source # rvarT :: StdUniform Int16 -> RVarT n Int16 Source #
Distribution StdUniform Int32 Source #
Methods rvar :: StdUniform Int32 -> RVar Int32 Source # rvarT :: StdUniform Int32 -> RVarT n Int32 Source #
Distribution StdUniform Int64 Source #
Methods rvar :: StdUniform Int64 -> RVar Int64 Source # rvarT :: StdUniform Int64 -> RVarT n Int64 Source #
Distribution StdUniform Ordering Source #
Methods rvar :: StdUniform Ordering -> RVar Ordering Source # rvarT :: StdUniform Ordering -> RVarT n Ordering Source #
Distribution StdUniform Word Source #
Methods rvar :: StdUniform Word -> RVar Word Source # rvarT :: StdUniform Word -> RVarT n Word Source #
Distribution StdUniform Word8 Source #
Methods rvar :: StdUniform Word8 -> RVar Word8 Source # rvarT :: StdUniform Word8 -> RVarT n Word8 Source #
Distribution StdUniform Word16 Source #
Methods rvar :: StdUniform Word16 -> RVar Word16 Source # rvarT :: StdUniform Word16 -> RVarT n Word16 Source #
Distribution StdUniform Word32 Source #
Methods rvar :: StdUniform Word32 -> RVar Word32 Source # rvarT :: StdUniform Word32 -> RVarT n Word32 Source #
Distribution StdUniform Word64 Source #
Methods rvar :: StdUniform Word64 -> RVar Word64 Source # rvarT :: StdUniform Word64 -> RVarT n Word64 Source #
Distribution StdUniform () Source #
Methods rvar :: StdUniform () -> RVar () Source # rvarT :: StdUniform () -> RVarT n () Source #
Distribution Uniform Bool Source #
Methods rvar :: Uniform Bool -> RVar Bool Source # rvarT :: Uniform Bool -> RVarT n Bool Source #
Distribution Uniform Char Source #
Methods rvar :: Uniform Char -> RVar Char Source # rvarT :: Uniform Char -> RVarT n Char Source #
Distribution Uniform Double Source #
Methods rvar :: Uniform Double -> RVar Double Source # rvarT :: Uniform Double -> RVarT n Double Source #
Distribution Uniform Float Source #
Methods rvar :: Uniform Float -> RVar Float Source # rvarT :: Uniform Float -> RVarT n Float Source #
Distribution Uniform Int Source #
Methods rvar :: Uniform Int -> RVar Int Source # rvarT :: Uniform Int -> RVarT n Int Source #
Distribution Uniform Int8 Source #
Methods rvar :: Uniform Int8 -> RVar Int8 Source # rvarT :: Uniform Int8 -> RVarT n Int8 Source #
Distribution Uniform Int16 Source #
Methods rvar :: Uniform Int16 -> RVar Int16 Source # rvarT :: Uniform Int16 -> RVarT n Int16 Source #
Distribution Uniform Int32 Source #
Methods rvar :: Uniform Int32 -> RVar Int32 Source # rvarT :: Uniform Int32 -> RVarT n Int32 Source #
Distribution Uniform Int64 Source #
Methods rvar :: Uniform Int64 -> RVar Int64 Source # rvarT :: Uniform Int64 -> RVarT n Int64 Source #
Distribution Uniform Integer Source #
Methods rvar :: Uniform Integer -> RVar Integer Source # rvarT :: Uniform Integer -> RVarT n Integer Source #
Distribution Uniform Ordering Source #
Methods rvar :: Uniform Ordering -> RVar Ordering Source # rvarT :: Uniform Ordering -> RVarT n Ordering Source #
Distribution Uniform Word Source #
Methods rvar :: Uniform Word -> RVar Word Source # rvarT :: Uniform Word -> RVarT n Word Source #
Distribution Uniform Word8 Source #
Methods rvar :: Uniform Word8 -> RVar Word8 Source # rvarT :: Uniform Word8 -> RVarT n Word8 Source #
Distribution Uniform Word16 Source #
Methods rvar :: Uniform Word16 -> RVar Word16 Source # rvarT :: Uniform Word16 -> RVarT n Word16 Source #
Distribution Uniform Word32 Source #
Methods rvar :: Uniform Word32 -> RVar Word32 Source # rvarT :: Uniform Word32 -> RVarT n Word32 Source #
Distribution Uniform Word64 Source #
Methods rvar :: Uniform Word64 -> RVar Word64 Source # rvarT :: Uniform Word64 -> RVarT n Word64 Source #
Distribution Uniform () Source #
Methods rvar :: Uniform () -> RVar () Source # rvarT :: Uniform () -> RVarT n () Source #
(Floating a, Distribution StdUniform a) => Distribution Exponential a Source #
Methods rvar :: Exponential a -> RVar a Source # rvarT :: Exponential a -> RVarT n a Source #
(Floating a, Distribution StdUniform a) => Distribution StretchedExponential a Source #
Methods rvar :: StretchedExponential a -> RVar a Source # rvarT :: StretchedExponential a -> RVarT n a Source #
Distribution Normal Double Source #
Methods rvar :: Normal Double -> RVar Double Source # rvarT :: Normal Double -> RVarT n Double Source #
Distribution Normal Float Source #
Methods rvar :: Normal Float -> RVar Float Source # rvarT :: Normal Float -> RVarT n Float Source #
(Floating a, Ord a, Distribution Normal a, Distribution StdUniform a) => Distribution Gamma a Source #
Methods rvar :: Gamma a -> RVar a Source # rvarT :: Gamma a -> RVarT n a Source #
Distribution Beta Double Source #
Methods rvar :: Beta Double -> RVar Double Source # rvarT :: Beta Double -> RVarT n Double Source #
Distribution Beta Float Source #
Methods rvar :: Beta Float -> RVar Float Source # rvarT :: Beta Float -> RVarT n Float Source #
(Fractional t, Distribution Gamma t) => Distribution ChiSquare t Source #
Methods rvar :: ChiSquare t -> RVar t Source # rvarT :: ChiSquare t -> RVarT n t Source #
(RealFloat a, Distribution StdUniform a) => Distribution Rayleigh a Source #
Methods rvar :: Rayleigh a -> RVar a Source # rvarT :: Rayleigh a -> RVarT n a Source #
(Floating a, Distribution Normal a, Distribution ChiSquare a) => Distribution T a Source #
Methods rvar :: T a -> RVar a Source # rvarT :: T a -> RVarT n a Source #
(RealFloat a, Ord a, Distribution StdUniform a) => Distribution Triangular a Source #
Methods rvar :: Triangular a -> RVar a Source # rvarT :: Triangular a -> RVarT n a Source #
(Floating a, Distribution StdUniform a) => Distribution Weibull a Source #
Methods rvar :: Weibull a -> RVar a Source # rvarT :: Weibull a -> RVarT n a Source #
(Floating a, Distribution StdUniform a) => Distribution Pareto a Source #
Methods rvar :: Pareto a -> RVar a Source # rvarT :: Pareto a -> RVarT n a Source #
HasResolution r => Distribution StdUniform (Fixed r) Source #
Methods rvar :: StdUniform (Fixed r) -> RVar (Fixed r) Source # rvarT :: StdUniform (Fixed r) -> RVarT n (Fixed r) Source #
HasResolution r => Distribution Uniform (Fixed r) Source #
Methods rvar :: Uniform (Fixed r) -> RVar (Fixed r) Source # rvarT :: Uniform (Fixed r) -> RVarT n (Fixed r) Source #
(Fractional a, Distribution Gamma a) => Distribution Dirichlet [a] Source #
Methods rvar :: Dirichlet [a] -> RVar [a] Source # rvarT :: Dirichlet [a] -> RVarT n [a] Source #
(Ord a, Fractional a, Distribution StdUniform a) => Distribution StdSimplex [a] Source #
Methods rvar :: StdSimplex [a] -> RVar [a] Source # rvarT :: StdSimplex [a] -> RVarT n [a] Source #
(Fractional b, Ord b, Distribution StdUniform b) => Distribution (Bernoulli b) Bool Source #
Methods rvar :: Bernoulli b Bool -> RVar Bool Source # rvarT :: Bernoulli b Bool -> RVarT n Bool Source #
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Word64 Source #
Methods rvar :: Bernoulli b0 Word64 -> RVar Word64 Source # rvarT :: Bernoulli b0 Word64 -> RVarT n Word64 Source #
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Word32 Source #
Methods rvar :: Bernoulli b0 Word32 -> RVar Word32 Source # rvarT :: Bernoulli b0 Word32 -> RVarT n Word32 Source #
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Word16 Source #
Methods rvar :: Bernoulli b0 Word16 -> RVar Word16 Source # rvarT :: Bernoulli b0 Word16 -> RVarT n Word16 Source #
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Word8 Source #
Methods rvar :: Bernoulli b0 Word8 -> RVar Word8 Source # rvarT :: Bernoulli b0 Word8 -> RVarT n Word8 Source #
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Word Source #
Methods rvar :: Bernoulli b0 Word -> RVar Word Source # rvarT :: Bernoulli b0 Word -> RVarT n Word Source #
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Int64 Source #
Methods rvar :: Bernoulli b0 Int64 -> RVar Int64 Source # rvarT :: Bernoulli b0 Int64 -> RVarT n Int64 Source #
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Int32 Source #
Methods rvar :: Bernoulli b0 Int32 -> RVar Int32 Source # rvarT :: Bernoulli b0 Int32 -> RVarT n Int32 Source #
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Int16 Source #
Methods rvar :: Bernoulli b0 Int16 -> RVar Int16 Source # rvarT :: Bernoulli b0 Int16 -> RVarT n Int16 Source #
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Int8 Source #
Methods rvar :: Bernoulli b0 Int8 -> RVar Int8 Source # rvarT :: Bernoulli b0 Int8 -> RVarT n Int8 Source #
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Int Source #
Methods rvar :: Bernoulli b0 Int -> RVar Int Source # rvarT :: Bernoulli b0 Int -> RVarT n Int Source #
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Integer Source #
Methods rvar :: Bernoulli b0 Integer -> RVar Integer Source # rvarT :: Bernoulli b0 Integer -> RVarT n Integer Source #
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Double Source #
Methods rvar :: Bernoulli b0 Double -> RVar Double Source # rvarT :: Bernoulli b0 Double -> RVarT n Double Source #
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Float Source #
Methods rvar :: Bernoulli b0 Float -> RVar Float Source # rvarT :: Bernoulli b0 Float -> RVarT n Float Source #
(Fractional p, Ord p, Distribution Uniform p) => Distribution (Categorical p) a Source #
Methods rvar :: Categorical p a -> RVar a Source # rvarT :: Categorical p a -> RVarT n a Source #
(Num t, Ord t, Vector v t) => Distribution (Ziggurat v) t Source #
Methods rvar :: Ziggurat v t -> RVar t Source # rvarT :: Ziggurat v t -> RVarT n t Source #
(Integral a, Floating b, Ord b, Distribution Normal b, Distribution StdUniform b) => Distribution (Erlang a) b Source #
Methods rvar :: Erlang a b -> RVar b Source # rvarT :: Erlang a b -> RVarT n b Source #
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Word64 Source #
Methods rvar :: Binomial b0 Word64 -> RVar Word64 Source # rvarT :: Binomial b0 Word64 -> RVarT n Word64 Source #
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Word32 Source #
Methods rvar :: Binomial b0 Word32 -> RVar Word32 Source # rvarT :: Binomial b0 Word32 -> RVarT n Word32 Source #
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Word16 Source #
Methods rvar :: Binomial b0 Word16 -> RVar Word16 Source # rvarT :: Binomial b0 Word16 -> RVarT n Word16 Source #
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Word8 Source #
Methods rvar :: Binomial b0 Word8 -> RVar Word8 Source # rvarT :: Binomial b0 Word8 -> RVarT n Word8 Source #
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Word Source #
Methods rvar :: Binomial b0 Word -> RVar Word Source # rvarT :: Binomial b0 Word -> RVarT n Word Source #
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Int64 Source #
Methods rvar :: Binomial b0 Int64 -> RVar Int64 Source # rvarT :: Binomial b0 Int64 -> RVarT n Int64 Source #
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Int32 Source #
Methods rvar :: Binomial b0 Int32 -> RVar Int32 Source # rvarT :: Binomial b0 Int32 -> RVarT n Int32 Source #
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Int16 Source #
Methods rvar :: Binomial b0 Int16 -> RVar Int16 Source # rvarT :: Binomial b0 Int16 -> RVarT n Int16 Source #
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Int8 Source #
Methods rvar :: Binomial b0 Int8 -> RVar Int8 Source # rvarT :: Binomial b0 Int8 -> RVarT n Int8 Source #
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Int Source #
Methods rvar :: Binomial b0 Int -> RVar Int Source # rvarT :: Binomial b0 Int -> RVarT n Int Source #
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Integer Source #
Methods rvar :: Binomial b0 Integer -> RVar Integer Source # rvarT :: Binomial b0 Integer -> RVarT n Integer Source #
Distribution (Binomial b0) Integer => Distribution (Binomial b0) Double Source #
Methods rvar :: Binomial b0 Double -> RVar Double Source # rvarT :: Binomial b0 Double -> RVarT n Double Source #
Distribution (Binomial b0) Integer => Distribution (Binomial b0) Float Source #
Methods rvar :: Binomial b0 Float -> RVar Float Source # rvarT :: Binomial b0 Float -> RVarT n Float Source #
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word64) b0, Distribution (Binomial b0) Word64) => Distribution (Poisson b0) Word64 Source #
Methods rvar :: Poisson b0 Word64 -> RVar Word64 Source # rvarT :: Poisson b0 Word64 -> RVarT n Word64 Source #
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word32) b0, Distribution (Binomial b0) Word32) => Distribution (Poisson b0) Word32 Source #
Methods rvar :: Poisson b0 Word32 -> RVar Word32 Source # rvarT :: Poisson b0 Word32 -> RVarT n Word32 Source #
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word16) b0, Distribution (Binomial b0) Word16) => Distribution (Poisson b0) Word16 Source #
Methods rvar :: Poisson b0 Word16 -> RVar Word16 Source # rvarT :: Poisson b0 Word16 -> RVarT n Word16 Source #
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word8) b0, Distribution (Binomial b0) Word8) => Distribution (Poisson b0) Word8 Source #
Methods rvar :: Poisson b0 Word8 -> RVar Word8 Source # rvarT :: Poisson b0 Word8 -> RVarT n Word8 Source #
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word) b0, Distribution (Binomial b0) Word) => Distribution (Poisson b0) Word Source #
Methods rvar :: Poisson b0 Word -> RVar Word Source # rvarT :: Poisson b0 Word -> RVarT n Word Source #
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int64) b0, Distribution (Binomial b0) Int64) => Distribution (Poisson b0) Int64 Source #
Methods rvar :: Poisson b0 Int64 -> RVar Int64 Source # rvarT :: Poisson b0 Int64 -> RVarT n Int64 Source #
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int32) b0, Distribution (Binomial b0) Int32) => Distribution (Poisson b0) Int32 Source #
Methods rvar :: Poisson b0 Int32 -> RVar Int32 Source # rvarT :: Poisson b0 Int32 -> RVarT n Int32 Source #
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int16) b0, Distribution (Binomial b0) Int16) => Distribution (Poisson b0) Int16 Source #
Methods rvar :: Poisson b0 Int16 -> RVar Int16 Source # rvarT :: Poisson b0 Int16 -> RVarT n Int16 Source #
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int8) b0, Distribution (Binomial b0) Int8) => Distribution (Poisson b0) Int8 Source #
Methods rvar :: Poisson b0 Int8 -> RVar Int8 Source # rvarT :: Poisson b0 Int8 -> RVarT n Int8 Source #
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int) b0, Distribution (Binomial b0) Int) => Distribution (Poisson b0) Int Source #
Methods rvar :: Poisson b0 Int -> RVar Int Source # rvarT :: Poisson b0 Int -> RVarT n Int Source #
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Integer) b0, Distribution (Binomial b0) Integer) => Distribution (Poisson b0) Integer Source #
Methods rvar :: Poisson b0 Integer -> RVar Integer Source # rvarT :: Poisson b0 Integer -> RVarT n Integer Source #
Distribution (Poisson b0) Integer => Distribution (Poisson b0) Double Source #
Methods rvar :: Poisson b0 Double -> RVar Double Source # rvarT :: Poisson b0 Double -> RVarT n Double Source #
Distribution (Poisson b0) Integer => Distribution (Poisson b0) Float Source #
Methods rvar :: Poisson b0 Float -> RVar Float Source # rvarT :: Poisson b0 Float -> RVarT n Float Source #
(Distribution (Bernoulli b) Bool, RealFloat a) => Distribution (Bernoulli b) (Complex a) Source #
Methods rvar :: Bernoulli b (Complex a) -> RVar (Complex a) Source # rvarT :: Bernoulli b (Complex a) -> RVarT n (Complex a) Source #
(Distribution (Bernoulli b) Bool, Integral a) => Distribution (Bernoulli b) (Ratio a) Source #
Methods rvar :: Bernoulli b (Ratio a) -> RVar (Ratio a) Source # rvarT :: Bernoulli b (Ratio a) -> RVarT n (Ratio a) Source #
(Num a, Eq a, Fractional p, Distribution (Binomial p) a) => Distribution (Multinomial p) [a] Source #
Methods rvar :: Multinomial p [a] -> RVar [a] Source # rvarT :: Multinomial p [a] -> RVarT n [a] Source #

class Distribution d t => PDF d t where Source #

Methods

pdf :: d t -> t -> Double Source #

logPdf :: d t -> t -> Double Source #

Instances

PDF StdUniform Double Source #
Methods pdf :: StdUniform Double -> Double -> Double Source # logPdf :: StdUniform Double -> Double -> Double Source #
PDF StdUniform Float Source #
Methods pdf :: StdUniform Float -> Float -> Double Source # logPdf :: StdUniform Float -> Float -> Double Source #
(Real a, Floating a, Distribution Normal a) => PDF Normal a Source #
Methods pdf :: Normal a -> a -> Double Source # logPdf :: Normal a -> a -> Double Source #
PDF Beta Double Source #
Methods pdf :: Beta Double -> Double -> Double Source # logPdf :: Beta Double -> Double -> Double Source #
PDF Beta Float Source #
Methods pdf :: Beta Float -> Float -> Double Source # logPdf :: Beta Float -> Float -> Double Source #
(Real b0, Distribution (Binomial b0) Word64) => PDF (Binomial b0) Word64 Source #
Methods pdf :: Binomial b0 Word64 -> Word64 -> Double Source # logPdf :: Binomial b0 Word64 -> Word64 -> Double Source #
(Real b0, Distribution (Binomial b0) Word32) => PDF (Binomial b0) Word32 Source #
Methods pdf :: Binomial b0 Word32 -> Word32 -> Double Source # logPdf :: Binomial b0 Word32 -> Word32 -> Double Source #
(Real b0, Distribution (Binomial b0) Word16) => PDF (Binomial b0) Word16 Source #
Methods pdf :: Binomial b0 Word16 -> Word16 -> Double Source # logPdf :: Binomial b0 Word16 -> Word16 -> Double Source #
(Real b0, Distribution (Binomial b0) Word8) => PDF (Binomial b0) Word8 Source #
Methods pdf :: Binomial b0 Word8 -> Word8 -> Double Source # logPdf :: Binomial b0 Word8 -> Word8 -> Double Source #
(Real b0, Distribution (Binomial b0) Word) => PDF (Binomial b0) Word Source #
Methods pdf :: Binomial b0 Word -> Word -> Double Source # logPdf :: Binomial b0 Word -> Word -> Double Source #
(Real b0, Distribution (Binomial b0) Int64) => PDF (Binomial b0) Int64 Source #
Methods pdf :: Binomial b0 Int64 -> Int64 -> Double Source # logPdf :: Binomial b0 Int64 -> Int64 -> Double Source #
(Real b0, Distribution (Binomial b0) Int32) => PDF (Binomial b0) Int32 Source #
Methods pdf :: Binomial b0 Int32 -> Int32 -> Double Source # logPdf :: Binomial b0 Int32 -> Int32 -> Double Source #
(Real b0, Distribution (Binomial b0) Int16) => PDF (Binomial b0) Int16 Source #
Methods pdf :: Binomial b0 Int16 -> Int16 -> Double Source # logPdf :: Binomial b0 Int16 -> Int16 -> Double Source #
(Real b0, Distribution (Binomial b0) Int8) => PDF (Binomial b0) Int8 Source #
Methods pdf :: Binomial b0 Int8 -> Int8 -> Double Source # logPdf :: Binomial b0 Int8 -> Int8 -> Double Source #
(Real b0, Distribution (Binomial b0) Int) => PDF (Binomial b0) Int Source #
Methods pdf :: Binomial b0 Int -> Int -> Double Source # logPdf :: Binomial b0 Int -> Int -> Double Source #
(Real b0, Distribution (Binomial b0) Integer) => PDF (Binomial b0) Integer Source #
Methods pdf :: Binomial b0 Integer -> Integer -> Double Source # logPdf :: Binomial b0 Integer -> Integer -> Double Source #
PDF (Binomial b0) Integer => PDF (Binomial b0) Double Source #
Methods pdf :: Binomial b0 Double -> Double -> Double Source # logPdf :: Binomial b0 Double -> Double -> Double Source #
PDF (Binomial b0) Integer => PDF (Binomial b0) Float Source #
Methods pdf :: Binomial b0 Float -> Float -> Double Source # logPdf :: Binomial b0 Float -> Float -> Double Source #

class Distribution d t => CDF d t where Source #

Minimal complete definition

cdf

Methods

cdf :: d t -> t -> Double Source #

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 Source #
Methods cdf :: StdUniform Bool -> Bool -> Double Source #
CDF StdUniform Char Source #
Methods cdf :: StdUniform Char -> Char -> Double Source #
CDF StdUniform Double Source #
Methods cdf :: StdUniform Double -> Double -> Double Source #
CDF StdUniform Float Source #
Methods cdf :: StdUniform Float -> Float -> Double Source #
CDF StdUniform Int Source #
Methods cdf :: StdUniform Int -> Int -> Double Source #
CDF StdUniform Int8 Source #
Methods cdf :: StdUniform Int8 -> Int8 -> Double Source #
CDF StdUniform Int16 Source #
Methods cdf :: StdUniform Int16 -> Int16 -> Double Source #
CDF StdUniform Int32 Source #
Methods cdf :: StdUniform Int32 -> Int32 -> Double Source #
CDF StdUniform Int64 Source #
Methods cdf :: StdUniform Int64 -> Int64 -> Double Source #
CDF StdUniform Ordering Source #
Methods cdf :: StdUniform Ordering -> Ordering -> Double Source #
CDF StdUniform Word Source #
Methods cdf :: StdUniform Word -> Word -> Double Source #
CDF StdUniform Word8 Source #
Methods cdf :: StdUniform Word8 -> Word8 -> Double Source #
CDF StdUniform Word16 Source #
Methods cdf :: StdUniform Word16 -> Word16 -> Double Source #
CDF StdUniform Word32 Source #
Methods cdf :: StdUniform Word32 -> Word32 -> Double Source #
CDF StdUniform Word64 Source #
Methods cdf :: StdUniform Word64 -> Word64 -> Double Source #
CDF StdUniform () Source #
Methods cdf :: StdUniform () -> () -> Double Source #
CDF Uniform Bool Source #
Methods cdf :: Uniform Bool -> Bool -> Double Source #
CDF Uniform Char Source #
Methods cdf :: Uniform Char -> Char -> Double Source #
CDF Uniform Double Source #
Methods cdf :: Uniform Double -> Double -> Double Source #
CDF Uniform Float Source #
Methods cdf :: Uniform Float -> Float -> Double Source #
CDF Uniform Int Source #
Methods cdf :: Uniform Int -> Int -> Double Source #
CDF Uniform Int8 Source #
Methods cdf :: Uniform Int8 -> Int8 -> Double Source #
CDF Uniform Int16 Source #
Methods cdf :: Uniform Int16 -> Int16 -> Double Source #
CDF Uniform Int32 Source #
Methods cdf :: Uniform Int32 -> Int32 -> Double Source #
CDF Uniform Int64 Source #
Methods cdf :: Uniform Int64 -> Int64 -> Double Source #
CDF Uniform Integer Source #
Methods cdf :: Uniform Integer -> Integer -> Double Source #
CDF Uniform Ordering Source #
Methods cdf :: Uniform Ordering -> Ordering -> Double Source #
CDF Uniform Word Source #
Methods cdf :: Uniform Word -> Word -> Double Source #
CDF Uniform Word8 Source #
Methods cdf :: Uniform Word8 -> Word8 -> Double Source #
CDF Uniform Word16 Source #
Methods cdf :: Uniform Word16 -> Word16 -> Double Source #
CDF Uniform Word32 Source #
Methods cdf :: Uniform Word32 -> Word32 -> Double Source #
CDF Uniform Word64 Source #
Methods cdf :: Uniform Word64 -> Word64 -> Double Source #
CDF Uniform () Source #
Methods cdf :: Uniform () -> () -> Double Source #
(Real a, Distribution Exponential a) => CDF Exponential a Source #
Methods cdf :: Exponential a -> a -> Double Source #
(Real a, Distribution StretchedExponential a) => CDF StretchedExponential a Source #
Methods cdf :: StretchedExponential a -> a -> Double Source #
(Real a, Distribution Normal a) => CDF Normal a Source #
Methods cdf :: Normal a -> a -> Double Source #
(Real a, Distribution Gamma a) => CDF Gamma a Source #
Methods cdf :: Gamma a -> a -> Double Source #
(Real t, Distribution ChiSquare t) => CDF ChiSquare t Source #
Methods cdf :: ChiSquare t -> t -> Double Source #
(Real a, Distribution Rayleigh a) => CDF Rayleigh a Source #
Methods cdf :: Rayleigh a -> a -> Double Source #
(Real a, Distribution T a) => CDF T a Source #
Methods cdf :: T a -> a -> Double Source #
(RealFrac a, Distribution Triangular a) => CDF Triangular a Source #
Methods cdf :: Triangular a -> a -> Double Source #
(Real a, Distribution Weibull a) => CDF Weibull a Source #
Methods cdf :: Weibull a -> a -> Double Source #
(Real a, Distribution Pareto a) => CDF Pareto a Source #
Methods cdf :: Pareto a -> a -> Double Source #
HasResolution r => CDF StdUniform (Fixed r) Source #
Methods cdf :: StdUniform (Fixed r) -> Fixed r -> Double Source #
HasResolution r => CDF Uniform (Fixed r) Source #
Methods cdf :: Uniform (Fixed r) -> Fixed r -> Double Source #
(Distribution (Bernoulli b) Bool, Real b) => CDF (Bernoulli b) Bool Source #
Methods cdf :: Bernoulli b Bool -> Bool -> Double Source #
CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Word64 Source #
Methods cdf :: Bernoulli b0 Word64 -> Word64 -> Double Source #
CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Word32 Source #
Methods cdf :: Bernoulli b0 Word32 -> Word32 -> Double Source #
CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Word16 Source #
Methods cdf :: Bernoulli b0 Word16 -> Word16 -> Double Source #
CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Word8 Source #
Methods cdf :: Bernoulli b0 Word8 -> Word8 -> Double Source #
CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Word Source #
Methods cdf :: Bernoulli b0 Word -> Word -> Double Source #
CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Int64 Source #
Methods cdf :: Bernoulli b0 Int64 -> Int64 -> Double Source #
CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Int32 Source #
Methods cdf :: Bernoulli b0 Int32 -> Int32 -> Double Source #
CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Int16 Source #
Methods cdf :: Bernoulli b0 Int16 -> Int16 -> Double Source #
CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Int8 Source #
Methods cdf :: Bernoulli b0 Int8 -> Int8 -> Double Source #
CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Int Source #
Methods cdf :: Bernoulli b0 Int -> Int -> Double Source #
CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Integer Source #
Methods cdf :: Bernoulli b0 Integer -> Integer -> Double Source #
CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Double Source #
Methods cdf :: Bernoulli b0 Double -> Double -> Double Source #
CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Float Source #
Methods cdf :: Bernoulli b0 Float -> Float -> Double Source #
(Integral a, Real b, Distribution (Erlang a) b) => CDF (Erlang a) b Source #
Methods cdf :: Erlang a b -> b -> Double Source #
(Real b0, Distribution (Binomial b0) Word64) => CDF (Binomial b0) Word64 Source #
Methods cdf :: Binomial b0 Word64 -> Word64 -> Double Source #
(Real b0, Distribution (Binomial b0) Word32) => CDF (Binomial b0) Word32 Source #
Methods cdf :: Binomial b0 Word32 -> Word32 -> Double Source #
(Real b0, Distribution (Binomial b0) Word16) => CDF (Binomial b0) Word16 Source #
Methods cdf :: Binomial b0 Word16 -> Word16 -> Double Source #
(Real b0, Distribution (Binomial b0) Word8) => CDF (Binomial b0) Word8 Source #
Methods cdf :: Binomial b0 Word8 -> Word8 -> Double Source #
(Real b0, Distribution (Binomial b0) Word) => CDF (Binomial b0) Word Source #
Methods cdf :: Binomial b0 Word -> Word -> Double Source #
(Real b0, Distribution (Binomial b0) Int64) => CDF (Binomial b0) Int64 Source #
Methods cdf :: Binomial b0 Int64 -> Int64 -> Double Source #
(Real b0, Distribution (Binomial b0) Int32) => CDF (Binomial b0) Int32 Source #
Methods cdf :: Binomial b0 Int32 -> Int32 -> Double Source #
(Real b0, Distribution (Binomial b0) Int16) => CDF (Binomial b0) Int16 Source #
Methods cdf :: Binomial b0 Int16 -> Int16 -> Double Source #
(Real b0, Distribution (Binomial b0) Int8) => CDF (Binomial b0) Int8 Source #
Methods cdf :: Binomial b0 Int8 -> Int8 -> Double Source #
(Real b0, Distribution (Binomial b0) Int) => CDF (Binomial b0) Int Source #
Methods cdf :: Binomial b0 Int -> Int -> Double Source #
(Real b0, Distribution (Binomial b0) Integer) => CDF (Binomial b0) Integer Source #
Methods cdf :: Binomial b0 Integer -> Integer -> Double Source #
CDF (Binomial b0) Integer => CDF (Binomial b0) Double Source #
Methods cdf :: Binomial b0 Double -> Double -> Double Source #
CDF (Binomial b0) Integer => CDF (Binomial b0) Float Source #
Methods cdf :: Binomial b0 Float -> Float -> Double Source #
(Real b0, Distribution (Poisson b0) Word64) => CDF (Poisson b0) Word64 Source #
Methods cdf :: Poisson b0 Word64 -> Word64 -> Double Source #
(Real b0, Distribution (Poisson b0) Word32) => CDF (Poisson b0) Word32 Source #
Methods cdf :: Poisson b0 Word32 -> Word32 -> Double Source #
(Real b0, Distribution (Poisson b0) Word16) => CDF (Poisson b0) Word16 Source #
Methods cdf :: Poisson b0 Word16 -> Word16 -> Double Source #
(Real b0, Distribution (Poisson b0) Word8) => CDF (Poisson b0) Word8 Source #
Methods cdf :: Poisson b0 Word8 -> Word8 -> Double Source #
(Real b0, Distribution (Poisson b0) Word) => CDF (Poisson b0) Word Source #
Methods cdf :: Poisson b0 Word -> Word -> Double Source #
(Real b0, Distribution (Poisson b0) Int64) => CDF (Poisson b0) Int64 Source #
Methods cdf :: Poisson b0 Int64 -> Int64 -> Double Source #
(Real b0, Distribution (Poisson b0) Int32) => CDF (Poisson b0) Int32 Source #
Methods cdf :: Poisson b0 Int32 -> Int32 -> Double Source #
(Real b0, Distribution (Poisson b0) Int16) => CDF (Poisson b0) Int16 Source #
Methods cdf :: Poisson b0 Int16 -> Int16 -> Double Source #
(Real b0, Distribution (Poisson b0) Int8) => CDF (Poisson b0) Int8 Source #
Methods cdf :: Poisson b0 Int8 -> Int8 -> Double Source #
(Real b0, Distribution (Poisson b0) Int) => CDF (Poisson b0) Int Source #
Methods cdf :: Poisson b0 Int -> Int -> Double Source #
(Real b0, Distribution (Poisson b0) Integer) => CDF (Poisson b0) Integer Source #
Methods cdf :: Poisson b0 Integer -> Integer -> Double Source #
CDF (Poisson b0) Integer => CDF (Poisson b0) Double Source #
Methods cdf :: Poisson b0 Double -> Double -> Double Source #
CDF (Poisson b0) Integer => CDF (Poisson b0) Float Source #
Methods cdf :: Poisson b0 Float -> Float -> Double Source #
(CDF (Bernoulli b) Bool, RealFloat a) => CDF (Bernoulli b) (Complex a) Source #
Methods cdf :: Bernoulli b (Complex a) -> Complex a -> Double Source #
(CDF (Bernoulli b) Bool, Integral a) => CDF (Bernoulli b) (Ratio a) Source #
Methods cdf :: Bernoulli b (Ratio a) -> Ratio a -> Double Source #