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pythonnumpymatplotlibprobability-distribution
Green Squirtle
Green Squirtle

Reputation: 65

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

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: enter image description here

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:

enter image description here

The graph I was expecting is the following: enter image description here

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

Upvotes: 0

Views: 397

Answers (2)

JohanC
JohanC

Reputation: 80279

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()

gaussian normal with histogram

Upvotes: 1

Terra
Terra

Reputation: 187

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()

Upvotes: 1

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