# statistics / Statistics / Distribution / Binomial.hs

The default branch has multiple heads

 ``` 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 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102``` ```{-# LANGUAGE DeriveDataTypeable, DeriveGeneric #-} -- | -- Module : Statistics.Distribution.Binomial -- Copyright : (c) 2009 Bryan O'Sullivan -- License : BSD3 -- -- Maintainer : bos@serpentine.com -- Stability : experimental -- Portability : portable -- -- The binomial distribution. This is the discrete probability -- distribution of the number of successes in a sequence of /n/ -- independent yes\/no experiments, each of which yields success with -- probability /p/. module Statistics.Distribution.Binomial ( BinomialDistribution -- * Constructors , binomial -- * Accessors , bdTrials , bdProbability ) where import Data.Data (Data, Typeable) import GHC.Generics (Generic) import qualified Statistics.Distribution as D import Numeric.SpecFunctions (choose) -- | The binomial distribution. data BinomialDistribution = BD { bdTrials :: {-# UNPACK #-} !Int -- ^ Number of trials. , bdProbability :: {-# UNPACK #-} !Double -- ^ Probability. } deriving (Eq, Read, Show, Typeable, Data, Generic) instance D.Distribution BinomialDistribution where cumulative = cumulative instance D.DiscreteDistr BinomialDistribution where probability = probability instance D.Mean BinomialDistribution where mean = mean instance D.Variance BinomialDistribution where variance = variance instance D.MaybeMean BinomialDistribution where maybeMean = Just . D.mean instance D.MaybeVariance BinomialDistribution where maybeStdDev = Just . D.stdDev maybeVariance = Just . D.variance -- This could be slow for big n probability :: BinomialDistribution -> Int -> Double probability (BD n p) k | k < 0 || k > n = 0 | n == 0 = 1 | otherwise = choose n k * p^k * (1-p)^(n-k) {-# INLINE probability #-} -- Summation from different sides required to reduce roundoff errors cumulative :: BinomialDistribution -> Double -> Double cumulative d@(BD n _) x | isNaN x = error "Statistics.Distribution.Binomial.cumulative: NaN input" | isInfinite x = if x > 0 then 1 else 0 | k < 0 = 0 | k >= n = 1 | k < m = D.sumProbabilities d 0 k | otherwise = 1 - D.sumProbabilities d (k+1) n where m = floor (mean d) k = floor x {-# INLINE cumulative #-} mean :: BinomialDistribution -> Double mean (BD n p) = fromIntegral n * p {-# INLINE mean #-} variance :: BinomialDistribution -> Double variance (BD n p) = fromIntegral n * p * (1 - p) {-# INLINE variance #-} -- | Construct binomial distribution. Number of trials must be -- non-negative and probability must be in [0,1] range binomial :: Int -- ^ Number of trials. -> Double -- ^ Probability. -> BinomialDistribution binomial n p | n < 0 = error \$ msg ++ "number of trials must be non-negative. Got " ++ show n | p < 0 || p > 1 = error \$ msg++"probability must be in [0,1] range. Got " ++ show p | otherwise = BD n p where msg = "Statistics.Distribution.Binomial.binomial: " {-# INLINE binomial #-} ```