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
|
-- |
-- Module : Statistics.Distribution.Poisson.Internal
-- Copyright : (c) 2011 Bryan O'Sullivan
-- License : BSD3
--
-- Maintainer : bos@serpentine.com
-- Stability : experimental
-- Portability : portable
--
-- Internal code for the Poisson distribution.
module Statistics.Distribution.Poisson.Internal
(
probability
) where
import Numeric.MathFunctions.Constants (m_sqrt_2_pi, m_tiny)
import Numeric.SpecFunctions (logGamma, stirlingError)
import Numeric.SpecFunctions.Extra (bd0)
-- | An unchecked, non-integer-valued version of Loader's saddle point
-- algorithm.
probability :: Double -> Double -> Double
probability 0 0 = 1
probability 0 1 = 0
probability lambda x
| isInfinite lambda = 0
| x < 0 = 0
| x <= lambda * m_tiny = exp (-lambda)
| lambda < x * m_tiny = exp (-lambda + x * log lambda - logGamma (x+1))
| otherwise = exp (-(stirlingError x) - bd0 x lambda) /
(m_sqrt_2_pi * sqrt x)
{-# INLINE probability #-}
|
