1
$\begingroup$

I recently encountered a strange situation while dealing with sampling :
Let's suppose I have X1 ... Xn random samples drawn from a population. Then I sort every samples and I make the sum of every samples. Why the sum sample seems to follow the same distribution as the original population and not a normal distribution ? Here is my python code if my question was not clear and an example with samples vs sorted samples :

n = 100
m= 100
k = 6

import numpy as np
import random 
import matplotlib.pyplot as plt

    
  
array2 = np.asarray([])
for j in range (200):
    array = np.asarray([0 for i in range(n)])  
    for i in range(m):
        sample = np.asarray([np.random.lognormal() for draw in range(n)])
        sample = np.sort(sample)
        array = np.add(array,sample)
    
    for element in array :
        array2 = np.append(array2, element)


plt.hist(array2, range(int(min(array2)), int(max(array2))))
plt.show()

non sorted

sorted

Many thanks in advance !!

$\endgroup$

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.