Data.Random.Distribution.Poisson

Documentation

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

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

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

Constructors

Poisson b

Instances

(Real b, Distribution (Poisson b) Integer) => CDF (Poisson b) Integer

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Integer -> Integer -> Double

(Real b, Distribution (Poisson b) Int) => CDF (Poisson b) Int

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Int8) => CDF (Poisson b) Int8

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Int16) => CDF (Poisson b) Int16

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Int32) => CDF (Poisson b) Int32

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Int64) => CDF (Poisson b) Int64

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Word) => CDF (Poisson b) Word

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Word8) => CDF (Poisson b) Word8

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Word16) => CDF (Poisson b) Word16

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Word32) => CDF (Poisson b) Word32

Defined in Data.Random.Distribution.Poisson

Methods

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

(Real b, Distribution (Poisson b) Word64) => CDF (Poisson b) Word64

Defined in Data.Random.Distribution.Poisson

Methods

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

CDF (Poisson b) Integer => CDF (Poisson b) Float

Defined in Data.Random.Distribution.Poisson

Methods

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

CDF (Poisson b) Integer => CDF (Poisson b) Double

Defined in Data.Random.Distribution.Poisson

Methods

cdf :: Poisson b Double -> Double -> Double

(Real b, Distribution (Poisson b) Integer) => PDF (Poisson b) Integer

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Integer -> Integer -> Double

logPdf :: Poisson b Integer -> Integer -> Double

(Real b, Distribution (Poisson b) Int) => PDF (Poisson b) Int

Defined in Data.Random.Distribution.Poisson

Methods

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

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

(Real b, Distribution (Poisson b) Int8) => PDF (Poisson b) Int8

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Int8 -> Int8 -> Double

logPdf :: Poisson b Int8 -> Int8 -> Double

(Real b, Distribution (Poisson b) Int16) => PDF (Poisson b) Int16

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Int16 -> Int16 -> Double

logPdf :: Poisson b Int16 -> Int16 -> Double

(Real b, Distribution (Poisson b) Int32) => PDF (Poisson b) Int32

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Int32 -> Int32 -> Double

logPdf :: Poisson b Int32 -> Int32 -> Double

(Real b, Distribution (Poisson b) Int64) => PDF (Poisson b) Int64

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Int64 -> Int64 -> Double

logPdf :: Poisson b Int64 -> Int64 -> Double

(Real b, Distribution (Poisson b) Word) => PDF (Poisson b) Word

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Word -> Word -> Double

logPdf :: Poisson b Word -> Word -> Double

(Real b, Distribution (Poisson b) Word8) => PDF (Poisson b) Word8

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Word8 -> Word8 -> Double

logPdf :: Poisson b Word8 -> Word8 -> Double

(Real b, Distribution (Poisson b) Word16) => PDF (Poisson b) Word16

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Word16 -> Word16 -> Double

logPdf :: Poisson b Word16 -> Word16 -> Double

(Real b, Distribution (Poisson b) Word32) => PDF (Poisson b) Word32

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Word32 -> Word32 -> Double

logPdf :: Poisson b Word32 -> Word32 -> Double

(Real b, Distribution (Poisson b) Word64) => PDF (Poisson b) Word64

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Word64 -> Word64 -> Double

logPdf :: Poisson b Word64 -> Word64 -> Double

PDF (Poisson b) Integer => PDF (Poisson b) Float

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Float -> Float -> Double

logPdf :: Poisson b Float -> Float -> Double

PDF (Poisson b) Integer => PDF (Poisson b) Double

Defined in Data.Random.Distribution.Poisson

Methods

pdf :: Poisson b Double -> Double -> Double

logPdf :: Poisson b Double -> Double -> Double

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

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Integer -> RVar Integer

rvarT :: Poisson b Integer -> RVarT n Integer

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

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Int -> RVar Int

rvarT :: Poisson b Int -> RVarT n Int

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

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Int8 -> RVar Int8

rvarT :: Poisson b Int8 -> RVarT n Int8

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

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Int16 -> RVar Int16

rvarT :: Poisson b Int16 -> RVarT n Int16

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

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Int32 -> RVar Int32

rvarT :: Poisson b Int32 -> RVarT n Int32

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

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Int64 -> RVar Int64

rvarT :: Poisson b Int64 -> RVarT n Int64

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

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Word -> RVar Word

rvarT :: Poisson b Word -> RVarT n Word

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

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Word8 -> RVar Word8

rvarT :: Poisson b Word8 -> RVarT n Word8

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

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Word16 -> RVar Word16

rvarT :: Poisson b Word16 -> RVarT n Word16

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

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Word32 -> RVar Word32

rvarT :: Poisson b Word32 -> RVarT n Word32

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

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Word64 -> RVar Word64

rvarT :: Poisson b Word64 -> RVarT n Word64

Distribution (Poisson b) Integer => Distribution (Poisson b) Float

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Float -> RVar Float

rvarT :: Poisson b Float -> RVarT n Float

Distribution (Poisson b) Integer => Distribution (Poisson b) Double

Defined in Data.Random.Distribution.Poisson

Methods

rvar :: Poisson b Double -> RVar Double

rvarT :: Poisson b Double -> RVarT n Double