eopen System.Numericeopen System.Numerics

​

let Fact n = 

    match n with

    | _ when n <= 1 -> 1I

    | _ -> [1I..BigInteger(n)] |> Seq.reduce ( * )

​

let CumulativeDistribution (x : int) (n : int) (p : float) =

    let EssentiallyZero = 10E-12

    let m = (float(n) * p) |> truncate |> int

    let CalcCurrent value k = 

        if k > m then 

            value * float(n - k + 1) * p / (float(k) * (1. - p))

        else

            value * float(k + 1) * (1. - p) / (float(n - k) * p)

    let Done k = if k > m then k > n else k < 0

    let NextK k = if k > m then k + 1 else k - 1

    let rec Calculate k totalUnscaledProbability previous unscaled =

        let current = CalcCurrent previous k

        let totalUnscaledProbability' = totalUnscaledProbability + current

        let unscaled' =

            if (k <= x) then

                unscaled + current

            else

                unscaled

        if (Done k) && (current <= EssentiallyZero) then

            unscaled', totalUnscaledProbability'

        else

            Calculate (NextK k) totalUnscaledProbability' current unscaled'   

    let InitialUnscaled = if (m <= x) then 1. else 0.

    let UnscaledResultAboveM, TotalUnscaledProbabilityAboveM = Calculate (m+1) 1. 1. InitialUnscaled

    let UnscaledResult, TotalUnscaledProbability = Calculate (m-1) TotalUnscaledProbabilityAboveM 1. UnscaledResultAboveM

    UnscaledResult / TotalUnscaledProbability

​

//printfn "Factorial of %A is %A" n (Fact n)

​

printfn "Binomial %f" (CumulativeDistribution 10 13 0.5)