Plotting of 1-dimensional Gaussian distribution function

Question

How do I make plots of a 1-dimensional Gaussian distribution function using the mean and standard deviation parameter values (μ, σ) = (−1, 1), (0, 2), and (2, 3)?

I\'m n

Answer 1

You are missing a parantheses in the denominator of your gaussian() function. As it is right now you divide by 2 and multiply with the variance (sig^2). But that is not true and as you can see of your plots the greater variance the more narrow the gaussian is - which is wrong, it should be opposit.

So just change the gaussian() function to:

def gaussian(x, mu, sig):
    return np.exp(-np.power(x - mu, 2.) / (2 * np.power(sig, 2.)))

Answer 2

In addition to previous answers, I recommend to first calculate the ratio in the exponent, then taking the square:

def gaussian(x,x0,sigma):
  return np.exp(-np.power((x - x0)/sigma, 2.)/2.)

That way, you can also calculate the gaussian of very small or very large numbers:

In: gaussian(1e-12,5e-12,3e-12)
Out: 0.64118038842995462

Answer 3

With the excellent matplotlib and numpy packages

from matplotlib import pyplot as mp
import numpy as np

def gaussian(x, mu, sig):
    return np.exp(-np.power(x - mu, 2.) / (2 * np.power(sig, 2.)))

x_values = np.linspace(-3, 3, 120)
for mu, sig in [(-1, 1), (0, 2), (2, 3)]:
    mp.plot(x_values, gaussian(x_values, mu, sig))

mp.show()

will produce something like

Answer 4

The correct form, based on the original syntax, and correctly normalized is:

def gaussian(x, mu, sig):
    return 1./(np.sqrt(2.*np.pi)*sig)*np.exp(-np.power((x - mu)/sig, 2.)/2)

Answer 5

you can read this tutorial for how to use functions of statistical distributions in python. http://docs.scipy.org/doc/scipy/reference/tutorial/stats.html

from scipy.stats import norm
import matplotlib.pyplot as plt
import numpy as np 

#initialize a normal distribution with frozen in mean=-1, std. dev.= 1
rv = norm(loc = -1., scale = 1.0)
rv1 = norm(loc = 0., scale = 2.0)
rv2 = norm(loc = 2., scale = 3.0)

x = np.arange(-10, 10, .1)

#plot the pdfs of these normal distributions 
plt.plot(x, rv.pdf(x), x, rv1.pdf(x), x, rv2.pdf(x))