Minkowski criterion function

minkowski.jl

julia> function L(c)
       sum([abs(xs-c)^2 for xs in x])/length(x)
       end
L (generic function with 2 methods)

julia> x=[1,2,3,4,5,6,9,12]
8-element Array{Int64,1}:
  1
  2
  3
  4
  5
  6
  9
 12

julia> mean(x)
5.25

You can see that the smallest error is in the 5.25 slot here

julia> [L(i) for i in 4:0.25:6]
9-element Array{Any,1}:
 13.5
 12.9375
 12.5
 12.1875
 12.0
 11.9375
 12.0
 12.1875
 12.5

Here is a method that brute forces it

julia> function optimizeL(x; p=2, start=minimum(x), stop=maximum(x), step=0.1)
           rng = [start:step:stop]
           res = [L(x,p,r) for r in rng]
           best = minimum(res)
           idx = findfirst(res, best)
           rng[idx]
       end

First though L needs to be defined better

julia> function L(x,p,c)
       sum([abs(xs-c)^p for xs in x])/length(x)
       end