Safe Haskell	None
Language	Haskell2010

Data.Random.Distribution.Poisson

Synopsis

integralPoisson :: (Integral a, RealFloat b, Distribution StdUniform b, Distribution (Erlang a) b, Distribution (Binomial b) a) => b -> RVarT m a
integralPoissonCDF :: (Integral a, Real b) => b -> a -> Double
integralPoissonPDF :: (Integral a, Real b) => b -> a -> Double
fractionalPoisson :: (Num a, Distribution (Poisson b) Integer) => b -> RVarT m a
fractionalPoissonCDF :: (CDF (Poisson b) Integer, RealFrac a) => b -> a -> Double
fractionalPoissonPDF :: (PDF (Poisson b) Integer, RealFrac a) => b -> a -> Double
poisson :: Distribution (Poisson b) a => b -> RVar a
poissonT :: Distribution (Poisson b) a => b -> RVarT m a
newtype Poisson b a = Poisson b

Documentation

integralPoisson :: (Integral a, RealFloat b, Distribution StdUniform b, Distribution (Erlang a) b, Distribution (Binomial b) a) => b -> RVarT m a Source #

integralPoissonCDF :: (Integral a, Real b) => b -> a -> Double Source #

integralPoissonPDF :: (Integral a, Real b) => b -> a -> Double Source #

The probability of getting exactly k successes is given by the probability mass function:

\[ f(k;\lambda) = \Pr(X = k) = \frac{\lambda^k e^{-\lambda}}{k!} \]

Note that in integralPoissonPDF the parameter of the mass function are given first and the range of the random variable distributed according to the Poisson distribution is given last. That is, \(f(2;0.5)\) is calculated by integralPoissonPDF 0.5 2.

fractionalPoisson :: (Num a, Distribution (Poisson b) Integer) => b -> RVarT m a Source #

fractionalPoissonCDF :: (CDF (Poisson b) Integer, RealFrac a) => b -> a -> Double Source #

fractionalPoissonPDF :: (PDF (Poisson b) Integer, RealFrac a) => b -> a -> Double Source #

poisson :: Distribution (Poisson b) a => b -> RVar a Source #

poissonT :: Distribution (Poisson b) a => b -> RVarT m a Source #

newtype Poisson b a Source #

Constructors

Poisson b

Instances

(Real b, Distribution (Poisson b) Integer) => CDF (Poisson b) Integer Source #
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Integer -> Integer -> Double Source #
(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 #
(Real b, Distribution (Poisson b) Integer) => PDF (Poisson b) Integer Source #
Instance details Defined in Data.Random.Distribution.Poisson Methods pdf :: Poisson b Integer -> Integer -> Double Source # logPdf :: Poisson b Integer -> Integer -> Double Source #
(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 Methods pdf :: Poisson b Int8 -> Int8 -> Double Source # logPdf :: Poisson b Int8 -> Int8 -> Double Source #
(Real b, Distribution (Poisson b) Int16) => PDF (Poisson b) Int16 Source #
Instance details Defined in Data.Random.Distribution.Poisson Methods pdf :: Poisson b Int16 -> Int16 -> Double Source # logPdf :: Poisson b Int16 -> Int16 -> Double Source #
(Real b, Distribution (Poisson b) Int32) => PDF (Poisson b) Int32 Source #
Instance details Defined in Data.Random.Distribution.Poisson Methods pdf :: Poisson b Int32 -> Int32 -> Double Source # logPdf :: Poisson b Int32 -> Int32 -> Double Source #
(Real b, Distribution (Poisson b) Int64) => PDF (Poisson b) Int64 Source #
Instance details Defined in Data.Random.Distribution.Poisson Methods pdf :: Poisson b Int64 -> Int64 -> Double Source # logPdf :: Poisson b Int64 -> Int64 -> Double Source #
(Real b, Distribution (Poisson b) Word) => PDF (Poisson b) Word Source #
Instance details Defined in Data.Random.Distribution.Poisson Methods pdf :: Poisson b Word -> Word -> Double Source # logPdf :: Poisson b Word -> Word -> Double Source #
(Real b, Distribution (Poisson b) Word8) => PDF (Poisson b) Word8 Source #
Instance details Defined in Data.Random.Distribution.Poisson Methods pdf :: Poisson b Word8 -> Word8 -> Double Source # logPdf :: Poisson b Word8 -> Word8 -> Double Source #
(Real b, Distribution (Poisson b) Word16) => PDF (Poisson b) Word16 Source #
Instance details Defined in Data.Random.Distribution.Poisson Methods pdf :: Poisson b Word16 -> Word16 -> Double Source # logPdf :: Poisson b Word16 -> Word16 -> Double Source #
(Real b, Distribution (Poisson b) Word32) => PDF (Poisson b) Word32 Source #
Instance details Defined in Data.Random.Distribution.Poisson Methods pdf :: Poisson b Word32 -> Word32 -> Double Source # logPdf :: Poisson b Word32 -> Word32 -> Double Source #
(Real b, Distribution (Poisson b) Word64) => PDF (Poisson b) Word64 Source #
Instance details Defined in Data.Random.Distribution.Poisson Methods pdf :: Poisson b Word64 -> Word64 -> Double Source # logPdf :: Poisson b Word64 -> Word64 -> Double Source #
PDF (Poisson b) Integer => PDF (Poisson b) Float Source #
Instance details Defined in Data.Random.Distribution.Poisson Methods pdf :: Poisson b Float -> Float -> Double Source # logPdf :: Poisson b Float -> Float -> Double Source #
PDF (Poisson b) Integer => PDF (Poisson b) Double Source #
Instance details Defined in Data.Random.Distribution.Poisson Methods pdf :: Poisson b Double -> Double -> Double Source # logPdf :: Poisson b Double -> Double -> Double Source #
(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 Methods rvar :: Poisson b Integer -> RVar Integer Source # rvarT :: Poisson b Integer -> RVarT n Integer Source #
(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 Methods rvar :: Poisson b Int -> RVar Int Source # rvarT :: Poisson b Int -> RVarT n Int Source #
(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 Methods rvar :: Poisson b Int8 -> RVar Int8 Source # rvarT :: Poisson b Int8 -> RVarT n Int8 Source #
(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 Methods rvar :: Poisson b Int16 -> RVar Int16 Source # rvarT :: Poisson b Int16 -> RVarT n Int16 Source #
(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 Methods rvar :: Poisson b Int32 -> RVar Int32 Source # rvarT :: Poisson b Int32 -> RVarT n Int32 Source #
(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 Methods rvar :: Poisson b Int64 -> RVar Int64 Source # rvarT :: Poisson b Int64 -> RVarT n Int64 Source #
(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 Methods rvar :: Poisson b Word -> RVar Word Source # rvarT :: Poisson b Word -> RVarT n Word Source #
(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 Methods rvar :: Poisson b Word8 -> RVar Word8 Source # rvarT :: Poisson b Word8 -> RVarT n Word8 Source #
(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 Methods rvar :: Poisson b Word16 -> RVar Word16 Source # rvarT :: Poisson b Word16 -> RVarT n Word16 Source #
(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 Methods rvar :: Poisson b Word32 -> RVar Word32 Source # rvarT :: Poisson b Word32 -> RVarT n Word32 Source #
(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 Methods rvar :: Poisson b Word64 -> RVar Word64 Source # rvarT :: Poisson b Word64 -> RVarT n Word64 Source #
Distribution (Poisson b) Integer => Distribution (Poisson b) Float Source #
Instance details Defined in Data.Random.Distribution.Poisson Methods rvar :: Poisson b Float -> RVar Float Source # rvarT :: Poisson b Float -> RVarT n Float Source #
Distribution (Poisson b) Integer => Distribution (Poisson b) Double Source #
Instance details Defined in Data.Random.Distribution.Poisson Methods rvar :: Poisson b Double -> RVar Double Source # rvarT :: Poisson b Double -> RVarT n Double Source #