Teorver task2

integrate.hs

import Data.Functor
import Data.Vector (fromList)
import qualified Data.Vector as V
import Statistics.Sample
import System.Random
import System.Random.Mersenne.Pure64
import Text.Printf

import Statistics.Distribution (quantile)
import Statistics.Distribution.Normal
import Statistics.Distribution.Uniform
import Statistics.Distribution.Exponential


gamma = 0.98

-- Общая функция для интегрирования
integrate :: (Double -> Double) -> [Double] -> Int -> (Double, Double)
integrate f smpl n = ( mean vals                                                                                   -- <- это оценка величины
                     , (quantile standard ((gamma+1) / 2)) * (stdDev vals) / (sqrt . fromIntegral $ V.length vals) -- <- вот здесь я считаю доверительный интервал
                     )
    where vals = f <$> fromList (take n smpl)


main = do
    -- Хороший генератор случайных чисел (вихрь Мерсенна)
    gen <- newPureMT

    -- Первый интеграл
    let f = \x -> (x^3)/2
        lambda = 2
        distr = exponential lambda
        n = 10^4
        (val, interval) = integrate f (genContList distr gen) n
    putStrLn $ formatAnswer n val interval

    -- Второй интеграл
    let f = \x -> (b-a) * (1/sqrt(1 + x^4))
        a = -4
        b = 5
        distr = uniformDistr a b
        n = 10^4
        (val, interval) = integrate f (genContList distr gen) n
    putStrLn $ formatAnswer n val interval

formatAnswer n val interval = printf "n = %d: %.4f ± %.4f (%.2f%%)" n val interval (interval/val * 100)


-------------------

class ContGenList d where
    genContList :: RandomGen g => d -> g -> [Double]

instance ContGenList UniformDistribution where
    genContList d gen = randomRs (uniformA d, uniformB d) gen

instance ContGenList ExponentialDistribution where
    genContList d gen = (\x -> log(x)/(-edLambda d)) <$> genContList (uniformDistr 0 1) gen