Safe Haskell	None
Language	Haskell2010

Math.Gamma

Synopsis

class (Eq a, Floating a, Factorial a) => Gamma a where
- gamma :: a -> a
- lnGamma :: a -> a
- lnFactorial :: Integral b => b -> a
class Num a => Factorial a where
- factorial :: Integral b => b -> a
class Gamma a => IncGamma a where
- lowerGamma :: a -> a -> a
- lnLowerGamma :: a -> a -> a
- p :: a -> a -> a
- upperGamma :: a -> a -> a
- lnUpperGamma :: a -> a -> a
- q :: a -> a -> a
class Gamma a => GenGamma a where
- generalizedGamma :: Int -> a -> a
- lnGeneralizedGamma :: Int -> a -> a

Documentation

class (Eq a, Floating a, Factorial a) => Gamma a where Source #

Gamma function. Minimal definition is ether gamma or lnGamma.

Minimal complete definition

Nothing

Methods

gamma :: a -> a Source #

The gamma function: gamma z == integral from 0 to infinity of t -> t**(z-1) * exp (negate t)

lnGamma :: a -> a Source #

Natural log of the gamma function

lnFactorial :: Integral b => b -> a Source #

Natural log of the factorial function

Instances

Gamma Double Source #
Instance details Defined in Math.Gamma Methods gamma :: Double -> Double Source # lnGamma :: Double -> Double Source # lnFactorial :: Integral b => b -> Double Source #
Gamma Float Source #
Instance details Defined in Math.Gamma Methods gamma :: Float -> Float Source # lnGamma :: Float -> Float Source # lnFactorial :: Integral b => b -> Float Source #
Gamma (Complex Double) Source #
Instance details Defined in Math.Gamma Methods gamma :: Complex Double -> Complex Double Source # lnGamma :: Complex Double -> Complex Double Source # lnFactorial :: Integral b => b -> Complex Double Source #
Gamma (Complex Float) Source #
Instance details Defined in Math.Gamma Methods gamma :: Complex Float -> Complex Float Source # lnGamma :: Complex Float -> Complex Float Source # lnFactorial :: Integral b => b -> Complex Float Source #

class Num a => Factorial a where Source #

Factorial function

Minimal complete definition

Nothing

Methods

factorial :: Integral b => b -> a Source #

Instances

Factorial Double Source #
Instance details Defined in Math.Factorial Methods factorial :: Integral b => b -> Double Source #
Factorial Float Source #
Instance details Defined in Math.Factorial Methods factorial :: Integral b => b -> Float Source #
Factorial Integer Source #
Instance details Defined in Math.Factorial Methods factorial :: Integral b => b -> Integer Source #
Factorial (Complex Double) Source #
Instance details Defined in Math.Factorial Methods factorial :: Integral b => b -> Complex Double Source #
Factorial (Complex Float) Source #
Instance details Defined in Math.Factorial Methods factorial :: Integral b => b -> Complex Float Source #

class Gamma a => IncGamma a where Source #

Incomplete gamma functions.

Methods

lowerGamma :: a -> a -> a Source #

Lower gamma function: lowerGamma s x == integral from 0 to x of t -> t**(s-1) * exp (negate t)

lnLowerGamma :: a -> a -> a Source #

Natural log of lower gamma function

p :: a -> a -> a Source #

Regularized lower incomplete gamma function: lowerGamma s x / gamma s

upperGamma :: a -> a -> a Source #

Upper gamma function: lowerGamma s x == integral from x to infinity of t -> t**(s-1) * exp (negate t)

lnUpperGamma :: a -> a -> a Source #

Natural log of upper gamma function

q :: a -> a -> a Source #

Regularized upper incomplete gamma function: upperGamma s x / gamma s

Instances

IncGamma Double Source #	I have not yet come up with a good strategy for evaluating these functions for negative `x`. They can be rather numerically unstable.
Instance details Defined in Math.Gamma Methods lowerGamma :: Double -> Double -> Double Source # lnLowerGamma :: Double -> Double -> Double Source # p :: Double -> Double -> Double Source # upperGamma :: Double -> Double -> Double Source # lnUpperGamma :: Double -> Double -> Double Source # q :: Double -> Double -> Double Source #
IncGamma Float Source #	This instance uses the Double instance.
Instance details Defined in Math.Gamma Methods lowerGamma :: Float -> Float -> Float Source # lnLowerGamma :: Float -> Float -> Float Source # p :: Float -> Float -> Float Source # upperGamma :: Float -> Float -> Float Source # lnUpperGamma :: Float -> Float -> Float Source # q :: Float -> Float -> Float Source #

class Gamma a => GenGamma a where Source #

Generalized gamma function (also known as multivariate gamma function). See http://en.wikipedia.org/wiki/Multivariate_gamma_function (Fetched Feb 29, 2012).

Methods

generalizedGamma :: Int -> a -> a Source #

Generalized gamma function. generalizedGamma p x = (pi ** ((p - 1) / 2)) * gamma x * generalizedGamma (p - 1) (x - 0.5)

lnGeneralizedGamma :: Int -> a -> a Source #

Natural log of generalizedGamma

Instances

GenGamma Double Source #
Instance details Defined in Math.Gamma Methods generalizedGamma :: Int -> Double -> Double Source # lnGeneralizedGamma :: Int -> Double -> Double Source #
GenGamma Float Source #
Instance details Defined in Math.Gamma Methods generalizedGamma :: Int -> Float -> Float Source # lnGeneralizedGamma :: Int -> Float -> Float Source #