Exploring implementation of kth central moments

moments.fsx

type moment_type =
    | CENTRAL
    | ZERO


let intToFloat intList = 
    intList 
    |> List.map (fun (i:int) -> (float i))

let ave intList = 
    intList 
    |> intToFloat 
    |> List.average

let moment offset_flag k (sample : float List) =

    let offset =
        match offset_flag with
        | CENTRAL -> List.average sample
        | ZERO -> 0.0

    let mean = 
        sample 
        |> List.average
    
    sample
    |> List.map (fun i -> pown (i - offset) k)
    |> List.average


let central_moment = moment CENTRAL
let zero_moment = moment ZERO

let bothMoments i = 
    [central_moment i; zero_moment i]

let first_moments = bothMoments 1 
let second_moments() = bothMoments 2 
let third_moments() = bothMoments 3

// sample use
let sample1 = [-5;-4;1;2;3;]
printfn "first moments (central | zero)  of %A are (%A | %A)" sample1 (sample1 |> intToFloat |> (List.iter |> first_moments))
printfn "second moments (central | zero)  of %A are (%A | %A)" sample1 (sample1 |> intToFloat |> second_moments)
printfn "third moments (central | zero)  of %A are (%A | %A)" sample1 (sample1 |> intToFloat |> third_moments)