statistics-0.16.4.0: 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 Source #

#### Instances

Instances details

FromJSON PoissonDistribution Source # |
Instance details Defined in Statistics.Distribution.Poisson Methods parseJSON :: Value -> Parser PoissonDistribution Source # parseJSONList :: Value -> Parser [PoissonDistribution] Source # omittedField :: Maybe PoissonDistribution Source #
ToJSON PoissonDistribution Source # |
Instance details Defined in Statistics.Distribution.Poisson Methods toJSON :: PoissonDistribution -> Value Source # toEncoding :: PoissonDistribution -> Encoding Source # toJSONList :: [PoissonDistribution] -> Value Source # toEncodingList :: [PoissonDistribution] -> Encoding Source # omitField :: PoissonDistribution -> Bool Source #
Binary PoissonDistribution Source # |
Instance details Defined in Statistics.Distribution.Poisson Methods put :: PoissonDistribution -> Put Source # get :: Get PoissonDistribution Source # putList :: [PoissonDistribution] -> Put Source #
Data PoissonDistribution Source # |

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 Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c PoissonDistribution Source #

toConstr :: PoissonDistribution -> Constr Source #

dataTypeOf :: PoissonDistribution -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c PoissonDistribution) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c PoissonDistribution) Source #

gmapT :: (forall b. Data b => b -> b) -> PoissonDistribution -> PoissonDistribution Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> PoissonDistribution -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> PoissonDistribution -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> PoissonDistribution -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> PoissonDistribution -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> PoissonDistribution -> m PoissonDistribution Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> PoissonDistribution -> m PoissonDistribution Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> PoissonDistribution -> m PoissonDistribution Source #

Generic PoissonDistribution Source # |

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-0.16.4.0-CwUrX7BVOPjWfNRlOxuPU" 'True) (C1 ('MetaCons "PD" 'PrefixI 'True) (S1 ('MetaSel ('Just "poissonLambda") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Double)))

Methods

from :: PoissonDistribution -> Rep PoissonDistribution x Source #

to :: Rep PoissonDistribution x -> PoissonDistribution Source #

Read PoissonDistribution Source # |
Instance details Defined in Statistics.Distribution.Poisson Methods readsPrec :: Int -> ReadS PoissonDistribution Source # readList :: ReadS [PoissonDistribution] Source # readPrec :: ReadPrec PoissonDistribution Source # readListPrec :: ReadPrec [PoissonDistribution] Source #
Show PoissonDistribution Source # |
Instance details Defined in Statistics.Distribution.Poisson Methods showsPrec :: Int -> PoissonDistribution -> ShowS Source # show :: PoissonDistribution -> String Source # showList :: [PoissonDistribution] -> ShowS Source #
Eq PoissonDistribution Source # |
Instance details Defined in Statistics.Distribution.Poisson Methods (==) :: PoissonDistribution -> PoissonDistribution -> Bool Source # (/=) :: PoissonDistribution -> PoissonDistribution -> Bool Source #
DiscreteDistr PoissonDistribution Source # |
Instance details Defined in Statistics.Distribution.Poisson Methods probability :: PoissonDistribution -> Int -> Double Source # logProbability :: PoissonDistribution -> Int -> Double Source #
Distribution PoissonDistribution Source # |
Instance details Defined in Statistics.Distribution.Poisson Methods cumulative :: PoissonDistribution -> Double -> Double Source # complCumulative :: PoissonDistribution -> Double -> Double Source #
Entropy PoissonDistribution Source # |
Instance details Defined in Statistics.Distribution.Poisson Methods entropy :: PoissonDistribution -> Double Source #
MaybeEntropy PoissonDistribution Source # |
Instance details Defined in Statistics.Distribution.Poisson Methods maybeEntropy :: PoissonDistribution -> Maybe Double Source #
MaybeMean PoissonDistribution Source # |
Instance details Defined in Statistics.Distribution.Poisson Methods maybeMean :: PoissonDistribution -> Maybe Double Source #
MaybeVariance PoissonDistribution Source # |
Instance details Defined in Statistics.Distribution.Poisson Methods maybeVariance :: PoissonDistribution -> Maybe Double Source # maybeStdDev :: PoissonDistribution -> Maybe Double Source #
Mean PoissonDistribution Source # |
Instance details Defined in Statistics.Distribution.Poisson Methods mean :: PoissonDistribution -> Double Source #
Variance PoissonDistribution Source # |
Instance details Defined in Statistics.Distribution.Poisson Methods variance :: PoissonDistribution -> Double Source # stdDev :: PoissonDistribution -> Double Source #
type Rep PoissonDistribution Source # |
Instance details Defined in Statistics.Distribution.Poisson type Rep PoissonDistribution = D1 ('MetaData "PoissonDistribution" "Statistics.Distribution.Poisson" "statistics-0.16.4.0-CwUrX7BVOPjWfNRlOxuPU" 'True) (C1 ('MetaCons "PD" 'PrefixI 'True) (S1 ('MetaSel ('Just "poissonLambda") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Double)))

# Constructors

poisson :: Double -> PoissonDistribution Source #

Create Poisson distribution.

poissonE :: Double -> Maybe PoissonDistribution Source #

Create Poisson distribution.

# Accessors

poissonLambda :: PoissonDistribution -> Double Source #

# 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