random-fu-0.2.7.7: Random number generation

Safe HaskellNone
LanguageHaskell2010

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.

Minimal complete definition

Nothing

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 # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution StdUniform Char Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution StdUniform Double Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution StdUniform Float Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution StdUniform Int Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution StdUniform Int8 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution StdUniform Int16 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution StdUniform Int32 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution StdUniform Int64 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution StdUniform Ordering Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution StdUniform Word Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution StdUniform Word8 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution StdUniform Word16 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution StdUniform Word32 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution StdUniform Word64 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution StdUniform () Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: StdUniform () -> RVar () Source #

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

Distribution Uniform Bool Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform Char Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform Double Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform Float Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform Int Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform Int8 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform Int16 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform Int32 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform Int64 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform Integer Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform Ordering Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform Word Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform Word8 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform Word16 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform Word32 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform Word64 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Distribution Uniform () Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

rvar :: Uniform () -> RVar () Source #

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

(Floating a, Distribution StdUniform a) => Distribution Weibull a Source # 
Instance details

Defined in Data.Random.Distribution.Weibull

Methods

rvar :: Weibull a -> RVar a Source #

rvarT :: Weibull a -> RVarT n a Source #

(RealFloat a, Ord a, Distribution StdUniform a) => Distribution Triangular a Source # 
Instance details

Defined in Data.Random.Distribution.Triangular

Methods

rvar :: Triangular a -> RVar a Source #

rvarT :: Triangular a -> RVarT n a Source #

(Floating a, Distribution StdUniform a) => Distribution StretchedExponential a Source # 
Instance details

Defined in Data.Random.Distribution.StretchedExponential

(RealFloat a, Distribution StdUniform a) => Distribution Rayleigh a Source # 
Instance details

Defined in Data.Random.Distribution.Rayleigh

Methods

rvar :: Rayleigh a -> RVar a Source #

rvarT :: Rayleigh a -> RVarT n a Source #

Distribution Normal Double Source # 
Instance details

Defined in Data.Random.Distribution.Normal

Distribution Normal Float Source # 
Instance details

Defined in Data.Random.Distribution.Normal

(Floating a, Ord a, Distribution Normal a, Distribution StdUniform a) => Distribution Gamma a Source # 
Instance details

Defined in Data.Random.Distribution.Gamma

Methods

rvar :: Gamma a -> RVar a Source #

rvarT :: Gamma a -> RVarT n a Source #

(Floating a, Distribution StdUniform a) => Distribution Exponential a Source # 
Instance details

Defined in Data.Random.Distribution.Exponential

Methods

rvar :: Exponential a -> RVar a Source #

rvarT :: Exponential a -> RVarT n a Source #

(Fractional t, Distribution Gamma t) => Distribution ChiSquare t Source # 
Instance details

Defined in Data.Random.Distribution.ChiSquare

Methods

rvar :: ChiSquare t -> RVar t Source #

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

(Floating a, Distribution Normal a, Distribution ChiSquare a) => Distribution T a Source # 
Instance details

Defined in Data.Random.Distribution.T

Methods

rvar :: T a -> RVar a Source #

rvarT :: T a -> RVarT n a Source #

Distribution Beta Double Source # 
Instance details

Defined in Data.Random.Distribution.Beta

Distribution Beta Float Source # 
Instance details

Defined in Data.Random.Distribution.Beta

(Floating a, Distribution StdUniform a) => Distribution Pareto a Source # 
Instance details

Defined in Data.Random.Distribution.Pareto

Methods

rvar :: Pareto a -> RVar a Source #

rvarT :: Pareto a -> RVarT n a Source #

HasResolution r => Distribution StdUniform (Fixed r) Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

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 # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

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

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

(Ord a, Fractional a, Distribution StdUniform a) => Distribution StdSimplex [a] Source # 
Instance details

Defined in Data.Random.Distribution.Simplex

Methods

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

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

(Fractional a, Distribution Gamma a) => Distribution Dirichlet [a] Source # 
Instance details

Defined in Data.Random.Distribution.Dirichlet

Methods

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

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

(Num t, Ord t, Vector v t) => Distribution (Ziggurat v) t Source # 
Instance details

Defined in Data.Random.Distribution.Ziggurat

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 # 
Instance details

Defined in Data.Random.Distribution.Gamma

Methods

rvar :: Erlang a b -> RVar b Source #

rvarT :: Erlang a b -> RVarT n b Source #

(Fractional p, Ord p, Distribution Uniform p) => Distribution (Categorical p) a Source # 
Instance details

Defined in Data.Random.Distribution.Categorical

Methods

rvar :: Categorical p a -> RVar a Source #

rvarT :: Categorical p a -> RVarT n a Source #

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Integer Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Int Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Int8 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Int16 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Int32 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Int64 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word8 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word16 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word32 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word64 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

Distribution (Binomial b) Integer => Distribution (Binomial b) Float Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

Distribution (Binomial b) Integer => Distribution (Binomial b) Double Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Integer) b, Distribution (Binomial b) Integer) => Distribution (Poisson b) Integer Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Int) b, Distribution (Binomial b) Int) => Distribution (Poisson b) Int Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Int8) b, Distribution (Binomial b) Int8) => Distribution (Poisson b) Int8 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Int16) b, Distribution (Binomial b) Int16) => Distribution (Poisson b) Int16 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Int32) b, Distribution (Binomial b) Int32) => Distribution (Poisson b) Int32 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Int64) b, Distribution (Binomial b) Int64) => Distribution (Poisson b) Int64 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Word) b, Distribution (Binomial b) Word) => Distribution (Poisson b) Word Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Word8) b, Distribution (Binomial b) Word8) => Distribution (Poisson b) Word8 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Word16) b, Distribution (Binomial b) Word16) => Distribution (Poisson b) Word16 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Word32) b, Distribution (Binomial b) Word32) => Distribution (Poisson b) Word32 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(RealFloat b, Distribution StdUniform b, Distribution (Erlang Word64) b, Distribution (Binomial b) Word64) => Distribution (Poisson b) Word64 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

Distribution (Poisson b) Integer => Distribution (Poisson b) Float Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

Distribution (Poisson b) Integer => Distribution (Poisson b) Double Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(Fractional b, Ord b, Distribution StdUniform b) => Distribution (Bernoulli b) Bool Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Integer Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Int Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Int8 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Int16 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Int32 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Int64 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Word Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Word8 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Word16 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Word32 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Word64 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Float Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Distribution (Bernoulli b) Bool => Distribution (Bernoulli b) Double Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

(Num a, Eq a, Fractional p, Distribution (Binomial p) a) => Distribution (Multinomial p) [a] Source # 
Instance details

Defined in Data.Random.Distribution.Multinomial

Methods

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

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

(Distribution (Bernoulli b) Bool, RealFloat a) => Distribution (Bernoulli b) (Complex a) Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

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 # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Methods

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

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

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

Minimal complete definition

Nothing

Methods

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

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

Instances
PDF StdUniform Double Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

PDF StdUniform Float Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

(Real a, Floating a, Distribution Normal a) => PDF Normal a Source # 
Instance details

Defined in Data.Random.Distribution.Normal

Methods

pdf :: Normal a -> a -> Double Source #

logPdf :: Normal a -> a -> Double Source #

PDF Beta Double Source # 
Instance details

Defined in Data.Random.Distribution.Beta

PDF Beta Float Source # 
Instance details

Defined in Data.Random.Distribution.Beta

(Real b, Distribution (Binomial b) Integer) => PDF (Binomial b) Integer Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Real b, Distribution (Binomial b) Int) => PDF (Binomial b) Int Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Real b, Distribution (Binomial b) Int8) => PDF (Binomial b) Int8 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Real b, Distribution (Binomial b) Int16) => PDF (Binomial b) Int16 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Real b, Distribution (Binomial b) Int32) => PDF (Binomial b) Int32 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Real b, Distribution (Binomial b) Int64) => PDF (Binomial b) Int64 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Real b, Distribution (Binomial b) Word) => PDF (Binomial b) Word Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Real b, Distribution (Binomial b) Word8) => PDF (Binomial b) Word8 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Real b, Distribution (Binomial b) Word16) => PDF (Binomial b) Word16 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Real b, Distribution (Binomial b) Word32) => PDF (Binomial b) Word32 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Real b, Distribution (Binomial b) Word64) => PDF (Binomial b) Word64 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

PDF (Binomial b) Integer => PDF (Binomial b) Float Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

PDF (Binomial b) Integer => PDF (Binomial b) Double Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Real b, Distribution (Poisson b) Integer) => PDF (Poisson b) Integer Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(Real b, Distribution (Poisson b) Int) => PDF (Poisson b) Int Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

Methods

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

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

(Real b, Distribution (Poisson b) Int8) => PDF (Poisson b) Int8 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(Real b, Distribution (Poisson b) Int16) => PDF (Poisson b) Int16 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(Real b, Distribution (Poisson b) Int32) => PDF (Poisson b) Int32 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(Real b, Distribution (Poisson b) Int64) => PDF (Poisson b) Int64 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(Real b, Distribution (Poisson b) Word) => PDF (Poisson b) Word Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(Real b, Distribution (Poisson b) Word8) => PDF (Poisson b) Word8 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(Real b, Distribution (Poisson b) Word16) => PDF (Poisson b) Word16 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(Real b, Distribution (Poisson b) Word32) => PDF (Poisson b) Word32 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(Real b, Distribution (Poisson b) Word64) => PDF (Poisson b) Word64 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

PDF (Poisson b) Integer => PDF (Poisson b) Float Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

PDF (Poisson b) Integer => PDF (Poisson b) Double Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

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

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 # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF StdUniform Char Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF StdUniform Double Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF StdUniform Float Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF StdUniform Int Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: StdUniform Int -> Int -> Double Source #

CDF StdUniform Int8 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF StdUniform Int16 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF StdUniform Int32 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF StdUniform Int64 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF StdUniform Ordering Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF StdUniform Word Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF StdUniform Word8 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF StdUniform Word16 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF StdUniform Word32 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF StdUniform Word64 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF StdUniform () Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

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

CDF Uniform Bool Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Bool -> Bool -> Double Source #

CDF Uniform Char Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Char -> Char -> Double Source #

CDF Uniform Double Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF Uniform Float Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Float -> Float -> Double Source #

CDF Uniform Int Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Int -> Int -> Double Source #

CDF Uniform Int8 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Int8 -> Int8 -> Double Source #

CDF Uniform Int16 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Int16 -> Int16 -> Double Source #

CDF Uniform Int32 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Int32 -> Int32 -> Double Source #

CDF Uniform Int64 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Int64 -> Int64 -> Double Source #

CDF Uniform Integer Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF Uniform Ordering Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF Uniform Word Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Word -> Word -> Double Source #

CDF Uniform Word8 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

cdf :: Uniform Word8 -> Word8 -> Double Source #

CDF Uniform Word16 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF Uniform Word32 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF Uniform Word64 Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

CDF Uniform () Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

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

(Real a, Distribution Weibull a) => CDF Weibull a Source # 
Instance details

Defined in Data.Random.Distribution.Weibull

Methods

cdf :: Weibull a -> a -> Double Source #

(RealFrac a, Distribution Triangular a) => CDF Triangular a Source # 
Instance details

Defined in Data.Random.Distribution.Triangular

Methods

cdf :: Triangular a -> a -> Double Source #

(Real a, Distribution StretchedExponential a) => CDF StretchedExponential a Source # 
Instance details

Defined in Data.Random.Distribution.StretchedExponential

Methods

cdf :: StretchedExponential a -> a -> Double Source #

(Real a, Distribution Rayleigh a) => CDF Rayleigh a Source # 
Instance details

Defined in Data.Random.Distribution.Rayleigh

Methods

cdf :: Rayleigh a -> a -> Double Source #

(Real a, Distribution Normal a) => CDF Normal a Source # 
Instance details

Defined in Data.Random.Distribution.Normal

Methods

cdf :: Normal a -> a -> Double Source #

(Real a, Distribution Gamma a) => CDF Gamma a Source # 
Instance details

Defined in Data.Random.Distribution.Gamma

Methods

cdf :: Gamma a -> a -> Double Source #

(Real a, Distribution Exponential a) => CDF Exponential a Source # 
Instance details

Defined in Data.Random.Distribution.Exponential

Methods

cdf :: Exponential a -> a -> Double Source #

(Real t, Distribution ChiSquare t) => CDF ChiSquare t Source # 
Instance details

Defined in Data.Random.Distribution.ChiSquare

Methods

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

(Real a, Distribution T a) => CDF T a Source # 
Instance details

Defined in Data.Random.Distribution.T

Methods

cdf :: T a -> a -> Double Source #

(Real a, Distribution Pareto a) => CDF Pareto a Source # 
Instance details

Defined in Data.Random.Distribution.Pareto

Methods

cdf :: Pareto a -> a -> Double Source #

HasResolution r => CDF StdUniform (Fixed r) Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

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

HasResolution r => CDF Uniform (Fixed r) Source # 
Instance details

Defined in Data.Random.Distribution.Uniform

Methods

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

(Integral a, Real b, Distribution (Erlang a) b) => CDF (Erlang a) b Source # 
Instance details

Defined in Data.Random.Distribution.Gamma

Methods

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

(Real b, Distribution (Binomial b) Integer) => CDF (Binomial b) Integer Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

(Real b, Distribution (Binomial b) Int) => CDF (Binomial b) Int Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

Methods

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

(Real b, Distribution (Binomial b) Int8) => CDF (Binomial b) Int8 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

Methods

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

(Real b, Distribution (Binomial b) Int16) => CDF (Binomial b) Int16 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

Methods

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

(Real b, Distribution (Binomial b) Int32) => CDF (Binomial b) Int32 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

Methods

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

(Real b, Distribution (Binomial b) Int64) => CDF (Binomial b) Int64 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

Methods

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

(Real b, Distribution (Binomial b) Word) => CDF (Binomial b) Word Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

Methods

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

(Real b, Distribution (Binomial b) Word8) => CDF (Binomial b) Word8 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

Methods

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

(Real b, Distribution (Binomial b) Word16) => CDF (Binomial b) Word16 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

Methods

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

(Real b, Distribution (Binomial b) Word32) => CDF (Binomial b) Word32 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

Methods

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

(Real b, Distribution (Binomial b) Word64) => CDF (Binomial b) Word64 Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

Methods

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

CDF (Binomial b) Integer => CDF (Binomial b) Float Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

Methods

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

CDF (Binomial b) Integer => CDF (Binomial b) Double Source # 
Instance details

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Double -> Double -> Double Source #

(Real b, Distribution (Poisson b) Integer) => CDF (Poisson b) Integer Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

(Real b, Distribution (Poisson b) Int) => CDF (Poisson b) Int Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Int8) => CDF (Poisson b) Int8 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Int16) => CDF (Poisson b) Int16 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Int32) => CDF (Poisson b) Int32 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Int64) => CDF (Poisson b) Int64 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Word) => CDF (Poisson b) Word Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Word8) => CDF (Poisson b) Word8 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Word16) => CDF (Poisson b) Word16 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Word32) => CDF (Poisson b) Word32 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Word64) => CDF (Poisson b) Word64 Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

Methods

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

CDF (Poisson b) Integer => CDF (Poisson b) Float Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

Methods

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

CDF (Poisson b) Integer => CDF (Poisson b) Double Source # 
Instance details

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Double -> Double -> Double Source #

(Distribution (Bernoulli b) Bool, Real b) => CDF (Bernoulli b) Bool Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Methods

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

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Integer Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Int Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Methods

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

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Int8 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Methods

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

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Int16 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Methods

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

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Int32 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Methods

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

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Int64 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Methods

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

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Word Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Methods

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

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Word8 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Methods

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

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Word16 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Word32 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Word64 Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Float Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Methods

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

CDF (Bernoulli b) Bool => CDF (Bernoulli b) Double Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

(CDF (Bernoulli b) Bool, RealFloat a) => CDF (Bernoulli b) (Complex a) Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Methods

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

(CDF (Bernoulli b) Bool, Integral a) => CDF (Bernoulli b) (Ratio a) Source # 
Instance details

Defined in Data.Random.Distribution.Bernoulli

Methods

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