random-fu-0.2.7.0: Random number generation

Safe HaskellNone
LanguageHaskell98

Data.Random.Distribution

Synopsis

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.

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 # 
Distribution StdUniform Char # 
Distribution StdUniform Double # 
Distribution StdUniform Float # 
Distribution StdUniform Int # 
Distribution StdUniform Int8 # 
Distribution StdUniform Int16 # 
Distribution StdUniform Int32 # 
Distribution StdUniform Int64 # 
Distribution StdUniform Ordering # 
Distribution StdUniform Word # 
Distribution StdUniform Word8 # 
Distribution StdUniform Word16 # 
Distribution StdUniform Word32 # 
Distribution StdUniform Word64 # 
Distribution StdUniform () # 

Methods

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

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

Distribution Uniform Bool # 
Distribution Uniform Char # 
Distribution Uniform Double # 
Distribution Uniform Float # 
Distribution Uniform Int # 

Methods

rvar :: Uniform Int -> RVar Int #

rvarT :: Uniform Int -> RVarT n Int #

Distribution Uniform Int8 # 
Distribution Uniform Int16 # 
Distribution Uniform Int32 # 
Distribution Uniform Int64 # 
Distribution Uniform Integer # 
Distribution Uniform Ordering # 
Distribution Uniform Word # 
Distribution Uniform Word8 # 
Distribution Uniform Word16 # 
Distribution Uniform Word32 # 
Distribution Uniform Word64 # 
Distribution Uniform () # 

Methods

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

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

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

Methods

rvar :: Exponential a -> RVar a #

rvarT :: Exponential a -> RVarT n a #

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

Methods

rvar :: Rayleigh a -> RVar a #

rvarT :: Rayleigh a -> RVarT n a #

(Floating a, Distribution StdUniform a) => Distribution StretchedExponential a # 
(RealFloat a, Ord a, Distribution StdUniform a) => Distribution Triangular a # 

Methods

rvar :: Triangular a -> RVar a #

rvarT :: Triangular a -> RVarT n a #

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

Methods

rvar :: Weibull a -> RVar a #

rvarT :: Weibull a -> RVarT n a #

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

Methods

rvar :: Gamma a -> RVar a #

rvarT :: Gamma a -> RVarT n a #

Distribution Beta Double # 
Distribution Beta Float # 
(Fractional t, Distribution Gamma t) => Distribution ChiSquare t # 

Methods

rvar :: ChiSquare t -> RVar t #

rvarT :: ChiSquare t -> RVarT n t #

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

Methods

rvar :: T a -> RVar a #

rvarT :: T a -> RVarT n a #

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

Methods

rvar :: Pareto a -> RVar a #

rvarT :: Pareto a -> RVarT n a #

HasResolution r => Distribution StdUniform (Fixed r) # 

Methods

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

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

HasResolution r => Distribution Uniform (Fixed r) # 

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] # 

Methods

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

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

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

Methods

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

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

(Fractional b, Ord b, Distribution StdUniform b) => Distribution (Bernoulli b) Bool # 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Word64 # 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Word32 # 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Word16 # 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Word8 # 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Word # 

Methods

rvar :: Bernoulli b0 Word -> RVar Word #

rvarT :: Bernoulli b0 Word -> RVarT n Word #

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Int64 # 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Int32 # 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Int16 # 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Int8 # 

Methods

rvar :: Bernoulli b0 Int8 -> RVar Int8 #

rvarT :: Bernoulli b0 Int8 -> RVarT n Int8 #

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Int # 

Methods

rvar :: Bernoulli b0 Int -> RVar Int #

rvarT :: Bernoulli b0 Int -> RVarT n Int #

Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Integer # 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Double # 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b0) Float # 
(Fractional p, Ord p, Distribution Uniform p) => Distribution (Categorical p) a # 

Methods

rvar :: Categorical p a -> RVar a #

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

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

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 # 

Methods

rvar :: Erlang a b -> RVar b #

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

(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Word64 # 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Word32 # 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Word16 # 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Word8 # 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Word # 

Methods

rvar :: Binomial b0 Word -> RVar Word #

rvarT :: Binomial b0 Word -> RVarT n Word #

(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Int64 # 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Int32 # 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Int16 # 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Int8 # 

Methods

rvar :: Binomial b0 Int8 -> RVar Int8 #

rvarT :: Binomial b0 Int8 -> RVarT n Int8 #

(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Int # 

Methods

rvar :: Binomial b0 Int -> RVar Int #

rvarT :: Binomial b0 Int -> RVarT n Int #

(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b0) Integer # 
Distribution (Binomial b0) Integer => Distribution (Binomial b0) Double # 
Distribution (Binomial b0) Integer => Distribution (Binomial b0) Float # 
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word64) b0, Distribution (Binomial b0) Word64) => Distribution (Poisson b0) Word64 # 
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word32) b0, Distribution (Binomial b0) Word32) => Distribution (Poisson b0) Word32 # 
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word16) b0, Distribution (Binomial b0) Word16) => Distribution (Poisson b0) Word16 # 
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word8) b0, Distribution (Binomial b0) Word8) => Distribution (Poisson b0) Word8 # 

Methods

rvar :: Poisson b0 Word8 -> RVar Word8 #

rvarT :: Poisson b0 Word8 -> RVarT n Word8 #

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word) b0, Distribution (Binomial b0) Word) => Distribution (Poisson b0) Word # 

Methods

rvar :: Poisson b0 Word -> RVar Word #

rvarT :: Poisson b0 Word -> RVarT n Word #

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int64) b0, Distribution (Binomial b0) Int64) => Distribution (Poisson b0) Int64 # 

Methods

rvar :: Poisson b0 Int64 -> RVar Int64 #

rvarT :: Poisson b0 Int64 -> RVarT n Int64 #

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int32) b0, Distribution (Binomial b0) Int32) => Distribution (Poisson b0) Int32 # 

Methods

rvar :: Poisson b0 Int32 -> RVar Int32 #

rvarT :: Poisson b0 Int32 -> RVarT n Int32 #

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int16) b0, Distribution (Binomial b0) Int16) => Distribution (Poisson b0) Int16 # 

Methods

rvar :: Poisson b0 Int16 -> RVar Int16 #

rvarT :: Poisson b0 Int16 -> RVarT n Int16 #

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int8) b0, Distribution (Binomial b0) Int8) => Distribution (Poisson b0) Int8 # 

Methods

rvar :: Poisson b0 Int8 -> RVar Int8 #

rvarT :: Poisson b0 Int8 -> RVarT n Int8 #

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int) b0, Distribution (Binomial b0) Int) => Distribution (Poisson b0) Int # 

Methods

rvar :: Poisson b0 Int -> RVar Int #

rvarT :: Poisson b0 Int -> RVarT n Int #

(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Integer) b0, Distribution (Binomial b0) Integer) => Distribution (Poisson b0) Integer # 
Distribution (Poisson b0) Integer => Distribution (Poisson b0) Double # 
Distribution (Poisson b0) Integer => Distribution (Poisson b0) Float # 

Methods

rvar :: Poisson b0 Float -> RVar Float #

rvarT :: Poisson b0 Float -> RVarT n Float #

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

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) # 

Methods

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

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

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

Methods

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

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

class Distribution d t => PDF d t where #

Methods

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

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

Instances

PDF StdUniform Double # 
PDF StdUniform Float # 
(Real a, Floating a, Distribution Normal a) => PDF Normal a # 

Methods

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

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

PDF Beta Double # 
PDF Beta Float # 

Methods

pdf :: Beta Float -> Float -> Double #

logPdf :: Beta Float -> Float -> Double #

(Real b0, Distribution (Binomial b0) Word64) => PDF (Binomial b0) Word64 # 
(Real b0, Distribution (Binomial b0) Word32) => PDF (Binomial b0) Word32 # 
(Real b0, Distribution (Binomial b0) Word16) => PDF (Binomial b0) Word16 # 
(Real b0, Distribution (Binomial b0) Word8) => PDF (Binomial b0) Word8 # 

Methods

pdf :: Binomial b0 Word8 -> Word8 -> Double #

logPdf :: Binomial b0 Word8 -> Word8 -> Double #

(Real b0, Distribution (Binomial b0) Word) => PDF (Binomial b0) Word # 

Methods

pdf :: Binomial b0 Word -> Word -> Double #

logPdf :: Binomial b0 Word -> Word -> Double #

(Real b0, Distribution (Binomial b0) Int64) => PDF (Binomial b0) Int64 # 

Methods

pdf :: Binomial b0 Int64 -> Int64 -> Double #

logPdf :: Binomial b0 Int64 -> Int64 -> Double #

(Real b0, Distribution (Binomial b0) Int32) => PDF (Binomial b0) Int32 # 

Methods

pdf :: Binomial b0 Int32 -> Int32 -> Double #

logPdf :: Binomial b0 Int32 -> Int32 -> Double #

(Real b0, Distribution (Binomial b0) Int16) => PDF (Binomial b0) Int16 # 

Methods

pdf :: Binomial b0 Int16 -> Int16 -> Double #

logPdf :: Binomial b0 Int16 -> Int16 -> Double #

(Real b0, Distribution (Binomial b0) Int8) => PDF (Binomial b0) Int8 # 

Methods

pdf :: Binomial b0 Int8 -> Int8 -> Double #

logPdf :: Binomial b0 Int8 -> Int8 -> Double #

(Real b0, Distribution (Binomial b0) Int) => PDF (Binomial b0) Int # 

Methods

pdf :: Binomial b0 Int -> Int -> Double #

logPdf :: Binomial b0 Int -> Int -> Double #

(Real b0, Distribution (Binomial b0) Integer) => PDF (Binomial b0) Integer # 
PDF (Binomial b0) Integer => PDF (Binomial b0) Double # 
PDF (Binomial b0) Integer => PDF (Binomial b0) Float # 

Methods

pdf :: Binomial b0 Float -> Float -> Double #

logPdf :: Binomial b0 Float -> Float -> Double #

class Distribution d t => CDF d t where #

Minimal complete definition

cdf

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 # 

Methods

cdf :: StdUniform Bool -> Bool -> Double #

CDF StdUniform Char # 

Methods

cdf :: StdUniform Char -> Char -> Double #

CDF StdUniform Double # 
CDF StdUniform Float # 

Methods

cdf :: StdUniform Float -> Float -> Double #

CDF StdUniform Int # 

Methods

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

CDF StdUniform Int8 # 

Methods

cdf :: StdUniform Int8 -> Int8 -> Double #

CDF StdUniform Int16 # 

Methods

cdf :: StdUniform Int16 -> Int16 -> Double #

CDF StdUniform Int32 # 

Methods

cdf :: StdUniform Int32 -> Int32 -> Double #

CDF StdUniform Int64 # 

Methods

cdf :: StdUniform Int64 -> Int64 -> Double #

CDF StdUniform Ordering # 
CDF StdUniform Word # 

Methods

cdf :: StdUniform Word -> Word -> Double #

CDF StdUniform Word8 # 

Methods

cdf :: StdUniform Word8 -> Word8 -> Double #

CDF StdUniform Word16 # 
CDF StdUniform Word32 # 
CDF StdUniform Word64 # 
CDF StdUniform () # 

Methods

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

CDF Uniform Bool # 

Methods

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

CDF Uniform Char # 

Methods

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

CDF Uniform Double # 

Methods

cdf :: Uniform Double -> Double -> Double #

CDF Uniform Float # 

Methods

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

CDF Uniform Int # 

Methods

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

CDF Uniform Int8 # 

Methods

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

CDF Uniform Int16 # 

Methods

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

CDF Uniform Int32 # 

Methods

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

CDF Uniform Int64 # 

Methods

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

CDF Uniform Integer # 

Methods

cdf :: Uniform Integer -> Integer -> Double #

CDF Uniform Ordering # 
CDF Uniform Word # 

Methods

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

CDF Uniform Word8 # 

Methods

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

CDF Uniform Word16 # 

Methods

cdf :: Uniform Word16 -> Word16 -> Double #

CDF Uniform Word32 # 

Methods

cdf :: Uniform Word32 -> Word32 -> Double #

CDF Uniform Word64 # 

Methods

cdf :: Uniform Word64 -> Word64 -> Double #

CDF Uniform () # 

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

HasResolution r => CDF StdUniform (Fixed r) # 

Methods

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

HasResolution r => CDF Uniform (Fixed r) # 

Methods

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

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

Methods

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

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Word64 # 

Methods

cdf :: Bernoulli b0 Word64 -> Word64 -> Double #

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Word32 # 

Methods

cdf :: Bernoulli b0 Word32 -> Word32 -> Double #

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Word16 # 

Methods

cdf :: Bernoulli b0 Word16 -> Word16 -> Double #

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Word8 # 

Methods

cdf :: Bernoulli b0 Word8 -> Word8 -> Double #

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Word # 

Methods

cdf :: Bernoulli b0 Word -> Word -> Double #

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Int64 # 

Methods

cdf :: Bernoulli b0 Int64 -> Int64 -> Double #

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Int32 # 

Methods

cdf :: Bernoulli b0 Int32 -> Int32 -> Double #

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Int16 # 

Methods

cdf :: Bernoulli b0 Int16 -> Int16 -> Double #

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Int8 # 

Methods

cdf :: Bernoulli b0 Int8 -> Int8 -> Double #

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Int # 

Methods

cdf :: Bernoulli b0 Int -> Int -> Double #

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Integer # 

Methods

cdf :: Bernoulli b0 Integer -> Integer -> Double #

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Double # 

Methods

cdf :: Bernoulli b0 Double -> Double -> Double #

CDF (Bernoulli b0) Bool => CDF (Bernoulli b0) Float # 

Methods

cdf :: Bernoulli b0 Float -> Float -> Double #

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

Methods

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

(Real b0, Distribution (Binomial b0) Word64) => CDF (Binomial b0) Word64 # 

Methods

cdf :: Binomial b0 Word64 -> Word64 -> Double #

(Real b0, Distribution (Binomial b0) Word32) => CDF (Binomial b0) Word32 # 

Methods

cdf :: Binomial b0 Word32 -> Word32 -> Double #

(Real b0, Distribution (Binomial b0) Word16) => CDF (Binomial b0) Word16 # 

Methods

cdf :: Binomial b0 Word16 -> Word16 -> Double #

(Real b0, Distribution (Binomial b0) Word8) => CDF (Binomial b0) Word8 # 

Methods

cdf :: Binomial b0 Word8 -> Word8 -> Double #

(Real b0, Distribution (Binomial b0) Word) => CDF (Binomial b0) Word # 

Methods

cdf :: Binomial b0 Word -> Word -> Double #

(Real b0, Distribution (Binomial b0) Int64) => CDF (Binomial b0) Int64 # 

Methods

cdf :: Binomial b0 Int64 -> Int64 -> Double #

(Real b0, Distribution (Binomial b0) Int32) => CDF (Binomial b0) Int32 # 

Methods

cdf :: Binomial b0 Int32 -> Int32 -> Double #

(Real b0, Distribution (Binomial b0) Int16) => CDF (Binomial b0) Int16 # 

Methods

cdf :: Binomial b0 Int16 -> Int16 -> Double #

(Real b0, Distribution (Binomial b0) Int8) => CDF (Binomial b0) Int8 # 

Methods

cdf :: Binomial b0 Int8 -> Int8 -> Double #

(Real b0, Distribution (Binomial b0) Int) => CDF (Binomial b0) Int # 

Methods

cdf :: Binomial b0 Int -> Int -> Double #

(Real b0, Distribution (Binomial b0) Integer) => CDF (Binomial b0) Integer # 

Methods

cdf :: Binomial b0 Integer -> Integer -> Double #

CDF (Binomial b0) Integer => CDF (Binomial b0) Double # 

Methods

cdf :: Binomial b0 Double -> Double -> Double #

CDF (Binomial b0) Integer => CDF (Binomial b0) Float # 

Methods

cdf :: Binomial b0 Float -> Float -> Double #

(Real b0, Distribution (Poisson b0) Word64) => CDF (Poisson b0) Word64 # 

Methods

cdf :: Poisson b0 Word64 -> Word64 -> Double #

(Real b0, Distribution (Poisson b0) Word32) => CDF (Poisson b0) Word32 # 

Methods

cdf :: Poisson b0 Word32 -> Word32 -> Double #

(Real b0, Distribution (Poisson b0) Word16) => CDF (Poisson b0) Word16 # 

Methods

cdf :: Poisson b0 Word16 -> Word16 -> Double #

(Real b0, Distribution (Poisson b0) Word8) => CDF (Poisson b0) Word8 # 

Methods

cdf :: Poisson b0 Word8 -> Word8 -> Double #

(Real b0, Distribution (Poisson b0) Word) => CDF (Poisson b0) Word # 

Methods

cdf :: Poisson b0 Word -> Word -> Double #

(Real b0, Distribution (Poisson b0) Int64) => CDF (Poisson b0) Int64 # 

Methods

cdf :: Poisson b0 Int64 -> Int64 -> Double #

(Real b0, Distribution (Poisson b0) Int32) => CDF (Poisson b0) Int32 # 

Methods

cdf :: Poisson b0 Int32 -> Int32 -> Double #

(Real b0, Distribution (Poisson b0) Int16) => CDF (Poisson b0) Int16 # 

Methods

cdf :: Poisson b0 Int16 -> Int16 -> Double #

(Real b0, Distribution (Poisson b0) Int8) => CDF (Poisson b0) Int8 # 

Methods

cdf :: Poisson b0 Int8 -> Int8 -> Double #

(Real b0, Distribution (Poisson b0) Int) => CDF (Poisson b0) Int # 

Methods

cdf :: Poisson b0 Int -> Int -> Double #

(Real b0, Distribution (Poisson b0) Integer) => CDF (Poisson b0) Integer # 

Methods

cdf :: Poisson b0 Integer -> Integer -> Double #

CDF (Poisson b0) Integer => CDF (Poisson b0) Double # 

Methods

cdf :: Poisson b0 Double -> Double -> Double #

CDF (Poisson b0) Integer => CDF (Poisson b0) Float # 

Methods

cdf :: Poisson b0 Float -> Float -> Double #

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

Methods

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

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

Methods

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