python: how do I draw a line graph of the following function?

Question

I'm new to python and I am trying to draw a graph for the probability of normal distribution of 1000 samples with specific mean and variance. The probability function is:

I have generated 1000 samples with:

import numpy as np
import matplotlib.pyplot as plt

s_mean = 0
s_variance = 0.1
s_std_dev = np.sqrt(s_variance)
s = np.random.normal(s_mean, 100, 1000)

I have managed to follow the function as much as I can:

prob_s = (np.exp(-1*((s-s_mean)**2)/(2*s_variance)))/(np.sqrt(2*np.pi)*s_std_dev)

and draw the graph using matplotlib:

f, (ax1) = plt.subplots(1, figsize=(5, 5))
ax1.hist(prob_s, bins=50, color='r')
plt.show()

but the graph is no where close to what I have expected:

The graph I was expecting is the following:

I can't find what's wrong here. Any help?

score 1 · Answer 1 · answered Jun 06 '21 at 13:13

That won't work. The normal distribution is specific, because it can not be expressed in terms of elementary functions. My advice is to just use scipy.stats

import matplotlib.pyplot as plt
import numpy as np
import scipy.stats as stats
import math

mu = 0
variance = 1
sigma = math.sqrt(variance)
x = np.linspace(mu - 3*sigma, mu + 3*sigma, 100)
plt.plot(x, stats.norm.pdf(x, mu, sigma))
plt.show()

if you want to draw the distribution out of those 1000 samples you should use

hist, bins = np.histogram(s, bins=50)
plt.plot(bins[1:], hist)
plt.show()

score 1 · Accepted Answer · answered Jun 06 '21 at 13:24

np.random.normal needs the mean and the standard deviation. Then s can be used as input for the histogram. density=True normalizes the histogram to be similar in size as a probability density function (pdf), so with an area of 1.

To draw the pdf curve, you can use your function, using some regularly-spaced x-values.

import numpy as np
import matplotlib.pyplot as plt

s_mean = 0
s_variance = 0.1
s_std_dev = np.sqrt(s_variance)
s = np.random.normal(s_mean, s_std_dev, 1000)

fig, ax1 = plt.subplots(figsize=(5, 5))
ax1.hist(s, bins=50, color='crimson', density=True)

x = np.linspace(s.min(), s.max(), 200)
prob_s = (np.exp(-1 * ((x - s_mean) ** 2) / (2 * s_variance))) / (np.sqrt(2 * np.pi) * s_std_dev)
ax1.plot(x, prob_s, color='dodgerblue')

plt.show()

python: how do I draw a line graph of the following function?

2 Answers2