random-fu-0.3.0.1: Random number generation

Safe Haskell | None
Language | Haskell2010

Data.Random.Distribution.Poisson

Synopsis

- integralPoisson :: forall a b (m :: Type -> Type). (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 :: forall a b (m :: Type -> Type). (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 :: forall b a (m :: Type -> Type). Distribution (Poisson b) a => b -> RVarT m a
- newtype Poisson b a = Poisson b

# Documentation

integralPoisson :: forall a b (m :: Type -> Type). (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 :: forall a b (m :: Type -> Type). (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 :: forall b a (m :: Type -> Type). Distribution (Poisson b) a => b -> RVarT m a Source #

newtype Poisson b a Source #

Constructors

Poisson b |

#### Instances

Instances details

(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) 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) 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 #
(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) Integer) => CDF (Poisson b) Integer Source # |
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Integer -> Integer -> 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 #
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 #
(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) Word) => CDF (Poisson b) Word Source # |
Instance details Defined in Data.Random.Distribution.Poisson Methods cdf :: Poisson b Word -> Word -> Double 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 :: forall (n :: Type -> Type). 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 :: forall (n :: Type -> Type). 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 :: forall (n :: Type -> Type). Poisson b Int64 -> RVarT n Int64 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 :: forall (n :: Type -> Type). Poisson b Int8 -> RVarT n Int8 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 :: forall (n :: Type -> Type). 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 :: forall (n :: Type -> Type). 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 :: forall (n :: Type -> Type). Poisson b Word64 -> RVarT n Word64 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 :: forall (n :: Type -> Type). Poisson b Word8 -> RVarT n Word8 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 :: forall (n :: Type -> Type). Poisson b Integer -> RVarT n Integer 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 :: forall (n :: Type -> Type). Poisson b Double -> RVarT n Double 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 :: forall (n :: Type -> Type). Poisson b Float -> RVarT n Float 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 :: forall (n :: Type -> Type). Poisson b Int -> RVarT n Int 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 :: forall (n :: Type -> Type). Poisson b Word -> RVarT n Word 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) 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) 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 #
(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) 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 #
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 #
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 #
(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) 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 #