module Statistics.Distribution.Binomial
(
BinomialDistribution
, binomial
, bdTrials
, bdProbability
) where
import Control.Exception (assert)
import Data.Typeable (Typeable)
import qualified Statistics.Distribution as D
import Statistics.Math (choose)
data BinomialDistribution = BD {
bdTrials :: !Int
, bdProbability :: !Double
} deriving (Eq, Read, Show, Typeable)
instance D.Distribution BinomialDistribution where
cumulative = cumulative
instance D.DiscreteDistr BinomialDistribution where
probability = probability
instance D.Variance BinomialDistribution where
variance = variance
instance D.Mean BinomialDistribution where
mean = mean
probability :: BinomialDistribution -> Int -> Double
probability (BD n p) k
| k < 0 || k > n = 0
| n == 0 = 1
| otherwise = choose n k * p^k * (1p)^(nk)
cumulative :: BinomialDistribution -> Double -> Double
cumulative d@(BD n _) x
| 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
mean :: BinomialDistribution -> Double
mean (BD n p) = fromIntegral n * p
variance :: BinomialDistribution -> Double
variance (BD n p) = fromIntegral n * p * (1 p)
binomial :: Int
-> Double
-> BinomialDistribution
binomial n p =
assert (n > 0) .
assert (p > 0 && p < 1) $
BD n p