Poisson distributions

Foundations of Probability in Python

Alexander A. Ramírez M.

CEO @ Synergy Vision

Poisson modeling

Call center

Line in a Bank

Poisson mass function plot

Call center photo

Imagine you have 2.2 calls per minute.

$$ $$ Poisson Probability mass function

In Python we do the following:

# Import poisson
from scipy.stats import poisson

# Calculate the probability mass 
# with pmf
poisson.pmf(k=3, mu=2.2)

0.19663867170702193

mu parameter specifies the mean of successful events.

Poisson Probability mass function

# Calculate pmf of 0
poisson.pmf(k=0, mu=2.2)

0.11080315836233387

# Calculate pmf of 6
poisson.pmf(k=6, mu=2.2)

0.01744840480280308

Poisson Probability mass function for different mu values

Cumulative distribution function

# Calculate cdf of 2
poisson.cdf(k=2, mu=2.2)

0.6227137499963162

# Calculate cdf of 5
poisson.cdf(k=5, mu=2.2)

0.9750902496952996

Survival function plot

# Calculate sf of 2
poisson.sf(k=2, mu=2.2)

0.3772862500036838

Percent point function plot

# Calculate ppf of 0.5
poisson.ppf(q=0.5, mu=2.2)

2.0

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

# Create the sample using poisson.rvs()
sample = poisson.rvs(mu=2.2, size=10000, random_state=13)

# Plot the sample
sns.distplot(sample, kde=False)
plt.show()

Poisson probability mass function plot

Foundations of Probability in Python