Statistics.Distribution.Poisson

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.

Documentation

data PoissonDistribution

Instances

Eq PoissonDistribution

Methods

(==) :: PoissonDistribution -> PoissonDistribution -> Bool

(/=) :: PoissonDistribution -> PoissonDistribution -> Bool

Data PoissonDistribution

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 :: (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

Read PoissonDistribution

Methods

readsPrec :: Int -> ReadS PoissonDistribution

readList :: ReadS [PoissonDistribution]

readPrec :: ReadPrec PoissonDistribution

readListPrec :: ReadPrec [PoissonDistribution]

Show PoissonDistribution

Methods

showsPrec :: Int -> PoissonDistribution -> ShowS

show :: PoissonDistribution -> String

showList :: [PoissonDistribution] -> ShowS

Generic PoissonDistribution

Associated Types

type Rep PoissonDistribution :: * -> *

Methods

from :: PoissonDistribution -> Rep PoissonDistribution x

to :: Rep PoissonDistribution x -> PoissonDistribution

ToJSON PoissonDistribution

Methods

toJSON :: PoissonDistribution -> Value

toEncoding :: PoissonDistribution -> Encoding

FromJSON PoissonDistribution

Methods

parseJSON :: Value -> Parser PoissonDistribution

Binary PoissonDistribution

Methods

put :: PoissonDistribution -> Put

get :: Get PoissonDistribution

putList :: [PoissonDistribution] -> Put

Entropy PoissonDistribution

Methods

entropy :: PoissonDistribution -> Double

MaybeEntropy PoissonDistribution

Methods

maybeEntropy :: PoissonDistribution -> Maybe Double

Variance PoissonDistribution

Methods

variance :: PoissonDistribution -> Double

stdDev :: PoissonDistribution -> Double

MaybeVariance PoissonDistribution

Methods

maybeVariance :: PoissonDistribution -> Maybe Double

maybeStdDev :: PoissonDistribution -> Maybe Double

Mean PoissonDistribution

Methods

mean :: PoissonDistribution -> Double

MaybeMean PoissonDistribution

Methods

maybeMean :: PoissonDistribution -> Maybe Double

DiscreteDistr PoissonDistribution

Methods

probability :: PoissonDistribution -> Int -> Double

logProbability :: PoissonDistribution -> Int -> Double

Distribution PoissonDistribution

Methods

cumulative :: PoissonDistribution -> Double -> Double

complCumulative :: PoissonDistribution -> Double -> Double

type Rep PoissonDistribution

type Rep PoissonDistribution = D1 (MetaData "PoissonDistribution" "Statistics.Distribution.Poisson" "statistics-0.13.3.0-4cjYwUsSjEQGDMfnb5oeqe" True) (C1 (MetaCons "PD" PrefixI True) (S1 (MetaSel (Just Symbol "poissonLambda") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Double)))

Constructors

poisson :: Double -> 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