Geometric distributions

Foundations of Probability in Python

Alexander A. Ramírez M.

CEO @ Synergy Vision

Geometric modeling

Basketball player free throw

Geometric distribution probability mass function plot

Model for a basketball player with probability 0.3 of scoring.

Geometric distribution probability mass function plot

We can model a grizzly bear that has a 0.033 probability of catching a salmon.

Geometric distribution probability mass function plot

In Python we code this as follows:

# Import geom
from scipy.stats import geom

# Calculate the probability mass 
# with pmf
geom.pmf(k=30, p=0.0333)

0.02455102908739612

p parameter specifies probability of success.

Geometric distribution cumulative distribution function

# Calculate cdf of 4
geom.cdf(k=4, p=0.3)

0.7598999999999999

Geometric distribution survival function

$$ $$

# Calculate sf of 2
geom.sf(k=2, p=0.3)

0.49000000000000005

Geometric distribution percent point function

$$ $$

# Calculate ppf of 0.6
geom.ppf(q=0.6, p=0.3)

3.0

# Import poisson, matplotlib.pyplot, and seaborn
from scipy.stats import geom
import matplotlib.pyplot as plt
import seaborn as sns

# Create the sample using geom.rvs()
sample = geom.rvs(p=0.3, size=10000, random_state=13)

# Plot the sample
sns.distplot(sample, bins = np.linspace(0,20,21), kde=False)
plt.show()

Geometric distribution sample histogram

Foundations of Probability in Python