CODEWITHSUNDEEP
pythondistributionsample
user12419639
user12419639

Reputation:

Python biased sample distribution

This is a very simple problem, but for some reason I'm going wrong somewhere and I can't figure it out. I need to show that the Mean Square Deviation is biased by drawing n = 10 values from a normal distribution and repeating N = 10,000 times. sigma = 1 and mu = 0. I want to plot a histogram of the 10,000 values. This is the equation I'm trying to model in Python:

(S_b)**2 = (1/n)*(∑,i=1,n, (X_i - X_bar)**2)

Here is the Python script I have so far:

import numpy as np
from matplotlib import pyplot as plt

N = 10000
sigma = 1
mu = 0
MSD = list() # Mean Square Deviation
n = 10
x = np.random.normal(n)*sigma+mu

for i in range(N):

    MSD.append((1/n)*(x[i] - np.mean(x))**2)
    
plt.hist(MSD,bins=50)
plt.title(r'$\overline {X}$', fontsize = 20)
plt.grid()

Right now I'm getting an error that says the float object is non-subscriptable, referring to the x[i] where I append the MSD. If I remove the [i], then I get a plot of 1 bin at 0, which is definitely not a distribution.

Where am I going wrong?

Upvotes: 0

Views: 516

Answers (1)

samlima
samlima

Reputation: 196

After the comments in the question, I believe I have understand the problem. So you want to get n random values and calculate the MSD of this sample N times. After that, you want to plot the result, right?

Here is the adaptation of your code

import numpy as np
from matplotlib import pyplot as plt

N = 10000
sigma = 1
mu = 0
MSD = list()  # Mean Square Deviation
n = 10

for i in range(N):
    x = np.random.normal(size=n) * sigma + mu
    MSD.append((1 / n) * sum((x - np.mean(x))**2))

plt.hist(MSD, bins=50)
plt.title(r'$\overline {X}$', fontsize=20)
plt.grid()

Here is the result of one execution:

enter image description here

Upvotes: 1

Related Questions