Examples of Data Distributions

Uniform Distribution



In [2]:

    
%matplotlib inline

import numpy as np
import matplotlib.pyplot as plt

values = np.random.uniform(-10.0, 10.0, 100000)
plt.hist(values, 50)
plt.show()

Normal / Gaussian

Visualize the probability density function:



In [3]:

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

x = np.arange(-3, 3, 0.001)
plt.plot(x, norm.pdf(x))









    Out[3]:





[<matplotlib.lines.Line2D at 0xde514e0>]

Generate some random numbers with a normal distribution. "mu" is the desired mean, "sigma" is the standard deviation:



In [4]:

    
import numpy as np
import matplotlib.pyplot as plt

mu = 5.0
sigma = 2.0
values = np.random.normal(mu, sigma, 10000)
plt.hist(values, 50)
plt.show()

Exponential PDF / "Power Law"



In [5]:

    
from scipy.stats import expon
import matplotlib.pyplot as plt

x = np.arange(0, 10, 0.001)
plt.plot(x, expon.pdf(x))









    Out[5]:





[<matplotlib.lines.Line2D at 0xe3304e0>]

Binomial Probability Mass Function



In [6]:

    
from scipy.stats import binom
import matplotlib.pyplot as plt

n, p = 10, 0.5
x = np.arange(0, 10, 0.001)
plt.plot(x, binom.pmf(x, n, p))









    Out[6]:





[<matplotlib.lines.Line2D at 0xe57ea20>]

Poisson Probability Mass Function

Example: My website gets on average 500 visits per day. What's the odds of getting 550?



In [7]:

    
from scipy.stats import poisson
import matplotlib.pyplot as plt

mu = 500
x = np.arange(400, 600, 0.5)
plt.plot(x, poisson.pmf(x, mu))









    Out[7]:





[<matplotlib.lines.Line2D at 0xe742e48>]

Pop Quiz!

What's the equivalent of a probability distribution function when using discrete instead of continuous data?



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