Algorithms For Dummies

Understanding distributions

Probability distribution is another idea that is important for working out better 

algorithms. A distribution is a table of values or a mathematical function that links 

every possible value of an input to the probability that such values could occur. 

Probability distributions are usually (but not solely) represented in charts whose 

abscissa axis represents the possible values of an input and whose ordinal axis 

represents the probability of occurrence. Most statistical models rely on the nor-

mal distributions, a distribution which is symmetric and has a characteristic bell 

shape. Representing a normal distribution in Python (as shown in Figure 17-1) 

requires a few lines of code. (You can find this code in the 

A4D; 17; Probability.

ipynb

 file on the Dummies site as part of the downloadable code; see the Intro-

duction for details.)

import numpy as np

from numpy.random import normal, uniform

import matplotlib.pyplot as plt

%matplotlib inline

normal_distribution = normal(size=10000) * 25 

+ 100

weights = np.ones_like(normal_distribution

                      ) / len(normal_distribution)

plt.hist(normal_distribution, bins=20, weights=weights)

plt.xlabel("Value")

plt.ylabel("Probability")

plt.show()

The plotted distribution represents an input of 10,000 numbers whose average is 

about 100. Each bar in the histogram represents the probability that a certain 

range of values will appear in the input. If you sum all the bars, you obtain the 

value of 1, which comprises all the probabilities expressed by the distribution.

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