statistics-0.16.2.1: A library of statistical types, data, and functions

Copyright | (c) 2009 2011 Bryan O'Sullivan
License | BSD3
Maintainer | bos@serpentine.com
Stability | experimental
Portability | portable
Safe Haskell | None
Language | Haskell2010

Statistics.Distribution.Poisson

Contents

- Constructors
- Accessors
- References

Description

The Poisson distribution. This is the discrete probability distribution of a number of events occurring in a fixed interval if these events occur with a known average rate, and occur independently from each other within that interval.

Synopsis

- data PoissonDistribution
- poisson :: Double -> PoissonDistribution
- poissonE :: Double -> Maybe PoissonDistribution
- poissonLambda :: PoissonDistribution -> Double

# Documentation

data PoissonDistribution #

#### Instances

Instances details

FromJSON PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Methods parseJSON :: Value -> Parser PoissonDistribution # parseJSONList :: Value -> Parser [PoissonDistribution] # omittedField :: Maybe PoissonDistribution #
ToJSON PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Methods toJSON :: PoissonDistribution -> Value # toEncoding :: PoissonDistribution -> Encoding # toJSONList :: [PoissonDistribution] -> Value # toEncodingList :: [PoissonDistribution] -> Encoding # omitField :: PoissonDistribution -> Bool #
Data PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> PoissonDistribution -> c PoissonDistribution # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c PoissonDistribution # toConstr :: PoissonDistribution -> Constr # dataTypeOf :: PoissonDistribution -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c PoissonDistribution) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c PoissonDistribution) # gmapT :: (forall b. Data b => b -> b) -> PoissonDistribution -> PoissonDistribution # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> PoissonDistribution -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> PoissonDistribution -> r # gmapQ :: (forall d. Data d => d -> u) -> PoissonDistribution -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> PoissonDistribution -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> PoissonDistribution -> m PoissonDistribution # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> PoissonDistribution -> m PoissonDistribution # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> PoissonDistribution -> m PoissonDistribution #
Generic PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Associated Types
type Rep PoissonDistribution |
Instance details Defined in Statistics.Distribution.Poisson type Rep PoissonDistribution = D1 ('MetaData "PoissonDistribution" "Statistics.Distribution.Poisson" "statistics-0.16.2.1-9EJt18csjGeB8Yk5f7eGk5" 'True) (C1 ('MetaCons "PD" 'PrefixI 'True) (S1 ('MetaSel ('Just "poissonLambda") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Double)))
Methods from :: PoissonDistribution -> Rep PoissonDistribution x # to :: Rep PoissonDistribution x -> PoissonDistribution #
Read PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Methods readsPrec :: Int -> ReadS PoissonDistribution # readList :: ReadS [PoissonDistribution] # readPrec :: ReadPrec PoissonDistribution # readListPrec :: ReadPrec [PoissonDistribution] #
Show PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Methods showsPrec :: Int -> PoissonDistribution -> ShowS # show :: PoissonDistribution -> String # showList :: [PoissonDistribution] -> ShowS #
Binary PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Methods put :: PoissonDistribution -> Put # get :: Get PoissonDistribution # putList :: [PoissonDistribution] -> Put #
Eq PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Methods (==) :: PoissonDistribution -> PoissonDistribution -> Bool # (/=) :: PoissonDistribution -> PoissonDistribution -> Bool #
DiscreteDistr PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Methods probability :: PoissonDistribution -> Int -> Double # logProbability :: PoissonDistribution -> Int -> Double #
Distribution PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Methods cumulative :: PoissonDistribution -> Double -> Double # complCumulative :: PoissonDistribution -> Double -> Double #
Entropy PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Methods entropy :: PoissonDistribution -> Double #
MaybeEntropy PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Methods maybeEntropy :: PoissonDistribution -> Maybe Double #
MaybeMean PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Methods maybeMean :: PoissonDistribution -> Maybe Double #
MaybeVariance PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Methods maybeVariance :: PoissonDistribution -> Maybe Double # maybeStdDev :: PoissonDistribution -> Maybe Double #
Mean PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Methods mean :: PoissonDistribution -> Double #
Variance PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson Methods variance :: PoissonDistribution -> Double # stdDev :: PoissonDistribution -> Double #
type Rep PoissonDistribution # |
Instance details Defined in Statistics.Distribution.Poisson type Rep PoissonDistribution = D1 ('MetaData "PoissonDistribution" "Statistics.Distribution.Poisson" "statistics-0.16.2.1-9EJt18csjGeB8Yk5f7eGk5" 'True) (C1 ('MetaCons "PD" 'PrefixI 'True) (S1 ('MetaSel ('Just "poissonLambda") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Double)))

# Constructors

poisson :: Double -> PoissonDistribution #

Create Poisson distribution.

poissonE :: Double -> Maybe PoissonDistribution #

Create Poisson distribution.

# Accessors

poissonLambda :: PoissonDistribution -> Double #

# References

- Loader, C. (2000) Fast and Accurate Computation of Binomial Probabilities. http://projects.scipy.org/scipy/raw-attachment/ticket/620/loader2000Fast.pdf
- Adell, J., Lekuona, A., and Yu, Y. (2010) Sharp Bounds on the Entropy of the Poisson Law and Related Quantities http://arxiv.org/pdf/1001.2897.pdf