summerschool_simtech_2023/material/1_mon/firststeps/statistic_functions.jl

#---
using ProgressMeter
import Base: length
function rse_sum(x)
    s = 0
    @showprogress for k = eachindex(x)
        s = s+x[k]
    end
    return s
end

rse_sum(1:36) == 666
#---

function rse_mean(x)
    return rse_sum(x) / length(x)
end

rse_mean(-15:17) == 1

#----
function rse_std(x)
   return  sqrt(rse_sum((x.-rse_mean(x)).^2)/(length(x)-1))
end
rse_std([1,2,3]) == 1

#----
function rse_tstat(x;σ = rse_std(x))
    return rse_mean(x)./ (σ / sqrt(length(x)))
end

rse_tstat(2:3) == 5

#---

struct StatResult
    x::Vector
    n::Int32
    std::Float64
    tvalue::Float64
end
Base.length(s::StatResult) = s.n
StatResult(x) = StatResult(x,length(x))

StatResult(x,n) =  StatResult(x,n,rse_std(x))
StatResult(x,n,std) = StatResult(x,n,std,rse_tstat(x;σ=std))


StatResult([10,500.]) # <1>

function tstat(x)
    return StatResult(length(x),rse_tstat(x))
end