Data.Random.Distribution

Documentation

class Distribution d t where

A definition of a random variable's distribution. From the distribution an RVar can be created, or the distribution can be directly sampled using sampleFrom or sample.

Methods

rvar :: d t -> RVar t

Return a random variable with this distribution.

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 Word8

Distribution StdUniform Word16

Distribution StdUniform Word32

Distribution StdUniform Word64

Distribution StdUniform ()

Distribution Uniform Bool

Distribution Uniform Char

Distribution Uniform Double

Distribution Uniform Float

Distribution Uniform Int

Distribution Uniform Int8

Distribution Uniform Int16

Distribution Uniform Int32

Distribution Uniform Int64

Distribution Uniform Integer

Distribution Uniform Ordering

Distribution Uniform Word8

Distribution Uniform Word16

Distribution Uniform Word32

Distribution Uniform Word64

Distribution Uniform ()

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

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

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

(Num t, Ord t, Storable t) => Distribution Ziggurat t

Distribution Normal Double

Distribution Normal Float

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

(Fractional a, Distribution Gamma a, Distribution StdUniform a) => Distribution Beta a

HasResolution r => Distribution StdUniform (Fixed r)

HasResolution r => Distribution Uniform (Fixed r)

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

Distribution (Bernoulli b[aqNA]) Bool => Distribution (Bernoulli b[aqNA]) Word64

Distribution (Bernoulli b[aqNA]) Bool => Distribution (Bernoulli b[aqNA]) Word32

Distribution (Bernoulli b[aqNA]) Bool => Distribution (Bernoulli b[aqNA]) Word16

Distribution (Bernoulli b[aqNA]) Bool => Distribution (Bernoulli b[aqNA]) Word8

Distribution (Bernoulli b[aqNA]) Bool => Distribution (Bernoulli b[aqNA]) Int64

Distribution (Bernoulli b[aqNA]) Bool => Distribution (Bernoulli b[aqNA]) Int32

Distribution (Bernoulli b[aqNA]) Bool => Distribution (Bernoulli b[aqNA]) Int16

Distribution (Bernoulli b[aqNA]) Bool => Distribution (Bernoulli b[aqNA]) Int8

Distribution (Bernoulli b[aqNA]) Bool => Distribution (Bernoulli b[aqNA]) Integer

Distribution (Bernoulli b[aqNA]) Bool => Distribution (Bernoulli b[aqNA]) Int

Distribution (Bernoulli b[ar4p]) Bool => Distribution (Bernoulli b[ar4p]) Double

Distribution (Bernoulli b[ar4p]) Bool => Distribution (Bernoulli b[ar4p]) Float

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

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

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

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

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

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

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

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

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

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

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

Distribution (Binomial b[aFwL]) Integer => Distribution (Binomial b[aFwL]) Double

Distribution (Binomial b[aFwL]) Integer => Distribution (Binomial b[aFwL]) Float

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

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

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

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

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

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

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

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

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

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

Distribution (Poisson b[aIn0]) Integer => Distribution (Poisson b[aIn0]) Double

Distribution (Poisson b[aIn0]) Integer => Distribution (Poisson b[aIn0]) Float

(Num p, Ord p, Distribution Uniform p) => Distribution (Discrete p) a

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

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

class Distribution d t => CDF d t where

Methods

cdf :: d t -> t -> Double

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

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

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

Thus, 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 tuple.

Instances

CDF StdUniform Bool

CDF StdUniform Char

CDF StdUniform Double

CDF StdUniform Float

CDF StdUniform Int

CDF StdUniform Int8

CDF StdUniform Int16

CDF StdUniform Int32

CDF StdUniform Int64

CDF StdUniform Ordering

CDF StdUniform Word8

CDF StdUniform Word16

CDF StdUniform Word32

CDF StdUniform Word64

CDF StdUniform ()

CDF Uniform Bool

CDF Uniform Char

CDF Uniform Double

CDF Uniform Float

CDF Uniform Int

CDF Uniform Int8

CDF Uniform Int16

CDF Uniform Int32

CDF Uniform Int64

CDF Uniform Integer

CDF Uniform Ordering

CDF Uniform Word8

CDF Uniform Word16

CDF Uniform Word32

CDF Uniform Word64

CDF Uniform ()

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

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

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

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

HasResolution r => CDF StdUniform (Fixed r)

HasResolution r => CDF Uniform (Fixed r)

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

CDF (Bernoulli b[aqNC]) Bool => CDF (Bernoulli b[aqNC]) Word64

CDF (Bernoulli b[aqNC]) Bool => CDF (Bernoulli b[aqNC]) Word32

CDF (Bernoulli b[aqNC]) Bool => CDF (Bernoulli b[aqNC]) Word16

CDF (Bernoulli b[aqNC]) Bool => CDF (Bernoulli b[aqNC]) Word8

CDF (Bernoulli b[aqNC]) Bool => CDF (Bernoulli b[aqNC]) Int64

CDF (Bernoulli b[aqNC]) Bool => CDF (Bernoulli b[aqNC]) Int32

CDF (Bernoulli b[aqNC]) Bool => CDF (Bernoulli b[aqNC]) Int16

CDF (Bernoulli b[aqNC]) Bool => CDF (Bernoulli b[aqNC]) Int8

CDF (Bernoulli b[aqNC]) Bool => CDF (Bernoulli b[aqNC]) Integer

CDF (Bernoulli b[aqNC]) Bool => CDF (Bernoulli b[aqNC]) Int

CDF (Bernoulli b[ar4r]) Bool => CDF (Bernoulli b[ar4r]) Double

CDF (Bernoulli b[ar4r]) Bool => CDF (Bernoulli b[ar4r]) Float

(Real b[aFcB], Distribution (Binomial b[aFcB]) Word64) => CDF (Binomial b[aFcB]) Word64

(Real b[aFcB], Distribution (Binomial b[aFcB]) Word32) => CDF (Binomial b[aFcB]) Word32

(Real b[aFcB], Distribution (Binomial b[aFcB]) Word16) => CDF (Binomial b[aFcB]) Word16

(Real b[aFcB], Distribution (Binomial b[aFcB]) Word8) => CDF (Binomial b[aFcB]) Word8

(Real b[aFcB], Distribution (Binomial b[aFcB]) Int64) => CDF (Binomial b[aFcB]) Int64

(Real b[aFcB], Distribution (Binomial b[aFcB]) Int32) => CDF (Binomial b[aFcB]) Int32

(Real b[aFcB], Distribution (Binomial b[aFcB]) Int16) => CDF (Binomial b[aFcB]) Int16

(Real b[aFcB], Distribution (Binomial b[aFcB]) Int8) => CDF (Binomial b[aFcB]) Int8

(Real b[aFcB], Distribution (Binomial b[aFcB]) Integer) => CDF (Binomial b[aFcB]) Integer

(Real b[aFcB], Distribution (Binomial b[aFcB]) Int) => CDF (Binomial b[aFcB]) Int

CDF (Binomial b[aFwO]) Integer => CDF (Binomial b[aFwO]) Double

CDF (Binomial b[aFwO]) Integer => CDF (Binomial b[aFwO]) Float

(Real b[aHYv], Distribution (Poisson b[aHYv]) Word64) => CDF (Poisson b[aHYv]) Word64

(Real b[aHYv], Distribution (Poisson b[aHYv]) Word32) => CDF (Poisson b[aHYv]) Word32

(Real b[aHYv], Distribution (Poisson b[aHYv]) Word16) => CDF (Poisson b[aHYv]) Word16

(Real b[aHYv], Distribution (Poisson b[aHYv]) Word8) => CDF (Poisson b[aHYv]) Word8

(Real b[aHYv], Distribution (Poisson b[aHYv]) Int64) => CDF (Poisson b[aHYv]) Int64

(Real b[aHYv], Distribution (Poisson b[aHYv]) Int32) => CDF (Poisson b[aHYv]) Int32

(Real b[aHYv], Distribution (Poisson b[aHYv]) Int16) => CDF (Poisson b[aHYv]) Int16

(Real b[aHYv], Distribution (Poisson b[aHYv]) Int8) => CDF (Poisson b[aHYv]) Int8

(Real b[aHYv], Distribution (Poisson b[aHYv]) Integer) => CDF (Poisson b[aHYv]) Integer

(Real b[aHYv], Distribution (Poisson b[aHYv]) Int) => CDF (Poisson b[aHYv]) Int

CDF (Poisson b[aIn2]) Integer => CDF (Poisson b[aIn2]) Double

CDF (Poisson b[aIn2]) Integer => CDF (Poisson b[aIn2]) Float

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

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

rvarT :: Distribution d t => 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.