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()
Many thanks in advance !!