Safe Haskell	None
Language	Haskell2010

Goal.Probability.Distributions.CoMPoisson

Contents

CoMPoisson
- Numerics

Description

Implementation of Conway-Maxwell Poisson distributions (CoMPoisson). (https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-9876.2005.00474.x) CoMPoisson distributions generalize Poisson distributions with a shape parameter that can concentrate or disperse the underlying Poisson distribution.

Synopsis

type CoMPoisson = LocationShape Poisson CoMShape
data CoMShape
comPoissonLogPartitionSum :: Double -> (Natural # CoMPoisson) -> Double
comPoissonExpectations :: KnownNat n => Double -> (Int -> Vector n Double) -> (Natural # CoMPoisson) -> Vector n Double

CoMPoisson

type CoMPoisson = LocationShape Poisson CoMShape Source #

The Manifold of CoMPoisson distributions. The Source coordinates of the CoMPoisson are the mode $mu$ and the "pseudo-precision" parameter $nu$, such that $mu / nu$ is approximately the variance of the distribution.

data CoMShape Source #

A type for storing the shape of a CoMPoisson distribution.

Instances

Instances details

Legendre CoMPoisson Source #
Instance details Defined in Goal.Probability.Distributions.CoMPoisson Methods potential :: (PotentialCoordinates CoMPoisson # CoMPoisson) -> Double
Manifold CoMShape Source #
Instance details Defined in Goal.Probability.Distributions.CoMPoisson Associated Types type Dimension CoMShape :: Nat
ExponentialFamily CoMPoisson Source #
Instance details Defined in Goal.Probability.Distributions.CoMPoisson Methods sufficientStatistic :: SamplePoint CoMPoisson -> Mean # CoMPoisson Source # averageSufficientStatistic :: Sample CoMPoisson -> Mean # CoMPoisson Source # logBaseMeasure :: Proxy CoMPoisson -> SamplePoint CoMPoisson -> Double Source #
AbsolutelyContinuous Natural CoMPoisson Source #
Instance details Defined in Goal.Probability.Distributions.CoMPoisson Methods logDensities :: Point Natural CoMPoisson -> Sample CoMPoisson -> [Double] Source # densities :: Point Natural CoMPoisson -> Sample CoMPoisson -> [Double] Source #
Transition c Source CoMPoisson => Generative c CoMPoisson Source #
Instance details Defined in Goal.Probability.Distributions.CoMPoisson Methods samplePoint :: Point c CoMPoisson -> Random (SamplePoint CoMPoisson) Source # sample :: Int -> Point c CoMPoisson -> Random (Sample CoMPoisson) Source #
Transition Natural Mean CoMPoisson Source #
Instance details Defined in Goal.Probability.Distributions.CoMPoisson Methods transition :: (Natural # CoMPoisson) -> Mean # CoMPoisson
Transition Natural Source CoMPoisson Source #
Instance details Defined in Goal.Probability.Distributions.CoMPoisson Methods transition :: (Natural # CoMPoisson) -> Source # CoMPoisson
Transition Source Mean CoMPoisson Source #
Instance details Defined in Goal.Probability.Distributions.CoMPoisson Methods transition :: (Source # CoMPoisson) -> Mean # CoMPoisson
Transition Source Natural CoMPoisson Source #
Instance details Defined in Goal.Probability.Distributions.CoMPoisson Methods transition :: (Source # CoMPoisson) -> Natural # CoMPoisson
LogLikelihood Natural CoMPoisson Int Source #
Instance details Defined in Goal.Probability.Distributions.CoMPoisson Methods logLikelihood :: [Int] -> (Natural # CoMPoisson) -> Double Source # logLikelihoodDifferential :: [Int] -> (Natural # CoMPoisson) -> Natural #* CoMPoisson Source #
type PotentialCoordinates CoMPoisson Source #
Instance details Defined in Goal.Probability.Distributions.CoMPoisson type PotentialCoordinates CoMPoisson = Natural
type Dimension CoMShape Source #
Instance details Defined in Goal.Probability.Distributions.CoMPoisson type Dimension CoMShape = 1

Numerics

comPoissonLogPartitionSum :: Double -> (Natural # CoMPoisson) -> Double Source #

Approximates the log-partition function of the given CoMPoisson distribution up to the specified precision.

comPoissonExpectations :: KnownNat n => Double -> (Int -> Vector n Double) -> (Natural # CoMPoisson) -> Vector n Double Source #

Approximates the expectations of functions given the natural parameters of a CoM-Poisson distribution.