estymator

import numpy
from matplotlib import pyplot
from scipy import  stats


def test (n,k,ns):
    r=stats.expon.rvs(loc =0, size = (ns,n),scale = 10)
    rr=numpy.sort(r, axis = 1)
    est_scale = (numpy.sum( rr[:,0:k],axis=1 )+(n-k)*rr[:,k-1])/k
    pyplot.figure()
    pyplot.hist(est_scale,bins = 30)
    pyplot.title( str(k)+" z "+str(n) )
    pyplot.show()
    print(n,k,numpy.mean(est_scale))


test(10,10,10000)
test(10,5,10000)
test(10,2,10000)

test(100,50,10000)
test(100,10,10000)
test(100,5,10000)
test(100,1,10000)