Data.Random.Distribution.Binomial

Documentation

integralBinomial :: (Integral a, Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => a -> b -> RVarT m a

integralBinomialCDF :: (Integral a, Real b) => a -> b -> a -> Double

integralBinomialPDF :: (Integral a, Real b) => a -> b -> a -> Double

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

\[ f(k;n,p) = \Pr(X = k) = \binom n k p^k(1-p)^{n-k} \]

Note that in integralBinomialPDF the parameters of the mass function are given first and the range of the random variable distributed according to the binomial distribution is given last. That is, \(f(2;4,0.5)\) is calculated by integralBinomialPDF 4 0.5 2.

integralBinomialLogPdf :: (Integral a, Real b) => a -> b -> a -> Double

We use the method given in "Fast and accurate computation of binomial probabilities, Loader, C", http://octave.1599824.n4.nabble.com/attachment/3829107/0/loader2000Fast.pdf

floatingBinomial :: (RealFrac a, Distribution (Binomial b) Integer) => a -> b -> RVar a

floatingBinomialCDF :: (CDF (Binomial b) Integer, RealFrac a) => a -> b -> a -> Double

floatingBinomialPDF :: (PDF (Binomial b) Integer, RealFrac a) => a -> b -> a -> Double

floatingBinomialLogPDF :: (PDF (Binomial b) Integer, RealFrac a) => a -> b -> a -> Double

binomial :: Distribution (Binomial b) a => a -> b -> RVar a

binomialT :: Distribution (Binomial b) a => a -> b -> RVarT m a

data Binomial b a

Constructors

Binomial a b

Instances

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

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Int16 -> Int16 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Int32 -> Int32 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Int64 -> Int64 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Int8 -> Int8 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Word16 -> Word16 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Word32 -> Word32 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Word64 -> Word64 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Word8 -> Word8 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Integer -> Integer -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Double -> Double -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Float -> Float -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Int -> Int -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

cdf :: Binomial b Word -> Word -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Int16 -> RVar Int16

rvarT :: forall (n :: Type -> Type). Binomial b Int16 -> RVarT n Int16

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

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Int32 -> RVar Int32

rvarT :: forall (n :: Type -> Type). Binomial b Int32 -> RVarT n Int32

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

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Int64 -> RVar Int64

rvarT :: forall (n :: Type -> Type). Binomial b Int64 -> RVarT n Int64

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

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Int8 -> RVar Int8

rvarT :: forall (n :: Type -> Type). Binomial b Int8 -> RVarT n Int8

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

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Word16 -> RVar Word16

rvarT :: forall (n :: Type -> Type). Binomial b Word16 -> RVarT n Word16

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

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Word32 -> RVar Word32

rvarT :: forall (n :: Type -> Type). Binomial b Word32 -> RVarT n Word32

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

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Word64 -> RVar Word64

rvarT :: forall (n :: Type -> Type). Binomial b Word64 -> RVarT n Word64

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

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Word8 -> RVar Word8

rvarT :: forall (n :: Type -> Type). Binomial b Word8 -> RVarT n Word8

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

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Integer -> RVar Integer

rvarT :: forall (n :: Type -> Type). Binomial b Integer -> RVarT n Integer

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

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Double -> RVar Double

rvarT :: forall (n :: Type -> Type). Binomial b Double -> RVarT n Double

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

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Float -> RVar Float

rvarT :: forall (n :: Type -> Type). Binomial b Float -> RVarT n Float

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

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Int -> RVar Int

rvarT :: forall (n :: Type -> Type). Binomial b Int -> RVarT n Int

(Floating b, Ord b, Distribution Beta b, Distribution StdUniform b) => Distribution (Binomial b) Word

Defined in Data.Random.Distribution.Binomial

Methods

rvar :: Binomial b Word -> RVar Word

rvarT :: forall (n :: Type -> Type). Binomial b Word -> RVarT n Word

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

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Int16 -> Int16 -> Double

logPdf :: Binomial b Int16 -> Int16 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Int32 -> Int32 -> Double

logPdf :: Binomial b Int32 -> Int32 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Int64 -> Int64 -> Double

logPdf :: Binomial b Int64 -> Int64 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Int8 -> Int8 -> Double

logPdf :: Binomial b Int8 -> Int8 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Word16 -> Word16 -> Double

logPdf :: Binomial b Word16 -> Word16 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Word32 -> Word32 -> Double

logPdf :: Binomial b Word32 -> Word32 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Word64 -> Word64 -> Double

logPdf :: Binomial b Word64 -> Word64 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Word8 -> Word8 -> Double

logPdf :: Binomial b Word8 -> Word8 -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Integer -> Integer -> Double

logPdf :: Binomial b Integer -> Integer -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Double -> Double -> Double

logPdf :: Binomial b Double -> Double -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Float -> Float -> Double

logPdf :: Binomial b Float -> Float -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Int -> Int -> Double

logPdf :: Binomial b Int -> Int -> Double

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

Defined in Data.Random.Distribution.Binomial

Methods

pdf :: Binomial b Word -> Word -> Double

logPdf :: Binomial b Word -> Word -> Double