Python Data Science Binomial Data Distribution

Binomial Distribution is a Discrete Distribution. It describes the outcome of binary scenarios, e.g. toss of a coin, it will either be head or tails.

It has following three parameters.

1. n - number of trials.

2. p - probability of occurence of each trial (e.g. for toss of a coin 0.5 each).

3. size - The shape of the returned array.

What is Discrete Distribution?

Discrete Distribution is defined at separate set of events, e.g. a coin toss's result is discrete as it can be only head or tails whereas height of people is continuous as it can be 170, 170.1, 170.11 and so on.

Example 1: Given 15 trials for coin toss generate 15 data points.

Code

from numpy import random

x = random.binomial(n=15, p=0.5, size=15)

print(x)

the output will be

[ 8 9 7 6 8 5 8 9 10 6 8 7 6 10 6]

Note: The output may differ everytime the code is run as it is generated at random.

Visualization of Binomial Distribution

Example 2: For the example above with 1000 data points.

Code

from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns

sns.distplot(random.binomial(n=10, p=0.5, size=1000), hist=True, kde=False)
plt.show()

the output will be

What is the Difference Between Normal and Binomial Distribution?

Normal distribution is continous whereas Binomial is discrete, but if there are enough data points it will be quite similar to normal distribution with certain loc and scale.

Example 3

Code

from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns

sns.distplot(random.normal(loc=50, scale=5, size=10000), hist=False)
sns.distplot(random.binomial(n=100, p=0.5, size=10000), hist=False)

plt.show()

the output will be

In the example above we draw the plot with 10000 data points and can observe from the fig that both the curve viz Normal distribution and Binomial distribution are displaying alot of similarities.