1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
|
{-# LANGUAGE DeriveDataTypeable #-}
-- |
-- Module : Statistics.Distribution.Poisson
-- Copyright : (c) 2009, 2011 Bryan O'Sullivan
-- License : BSD3
--
-- Maintainer : bos@serpentine.com
-- Stability : experimental
-- Portability : portable
--
-- 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.
module Statistics.Distribution.Poisson
(
PoissonDistribution
-- * Constructors
, poisson
-- * Accessors
, poissonLambda
-- * References
-- $references
) where
import Data.Typeable (Typeable)
import qualified Statistics.Distribution as D
import qualified Statistics.Distribution.Poisson.Internal as I
import Numeric.SpecFunctions (incompleteGamma)
newtype PoissonDistribution = PD {
poissonLambda :: Double
} deriving (Eq, Read, Show, Typeable)
instance D.Distribution PoissonDistribution where
cumulative (PD lambda) x
| x < 0 = 0
| otherwise = 1 - incompleteGamma (fromIntegral (floor x + 1 :: Int)) lambda
{-# INLINE cumulative #-}
instance D.DiscreteDistr PoissonDistribution where
probability (PD lambda) x = I.probability lambda (fromIntegral x)
{-# INLINE probability #-}
instance D.Variance PoissonDistribution where
variance = poissonLambda
{-# INLINE variance #-}
instance D.Mean PoissonDistribution where
mean = poissonLambda
{-# INLINE mean #-}
instance D.MaybeMean PoissonDistribution where
maybeMean = Just . D.mean
instance D.MaybeVariance PoissonDistribution where
maybeStdDev = Just . D.stdDev
-- | Create Poisson distribution.
poisson :: Double -> PoissonDistribution
poisson l
| l <= 0 = error $ "Statistics.Distribution.Poisson.poisson:\
\ lambda must be positive. Got " ++ show l
| otherwise = PD l
{-# INLINE poisson #-}
-- $references
--
-- * Loader, C. (2000) Fast and Accurate Computation of Binomial
-- Probabilities. <http://projects.scipy.org/scipy/raw-attachment/ticket/620/loader2000Fast.pdf>
|
