Exponential Distribution in Python
The Exponential Distribution is commonly used to model the time between events in a process where events occur continuously and independently at a constant average rate. It’s widely applied in scenarios such as:
- Time until failure of a machine component
- Time until the next customer arrives
- Time between phone calls at a call center
Parameters of Exponential Distribution:
- scale: The inverse of the rate parameter (λ) from the Poisson distribution. It defines the average time between events. The default value is 1.0.
- size: Specifies the output shape of the returned sample (i.e., the number of random values you want to generate).
Program:
Generating Samples
Let’s generate random numbers following an exponential distribution with:
- scale = 2.0
- size = (2, 3) (i.e., a 2x3 matrix)
from numpy import random
x = random.exponential(scale=2, size=(2, 3))
print(x)
Output:
[[0.55267412 0.48985355 1.48196931]
[3.16271856 0.71002355 1.13254062]]
Visualizing Exponential Distribution
We can also visualize the exponential distribution using Seaborn and Matplotlib:
Program:
from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns
sns.displot(random.exponential(size=1000), kind="kde")
plt.title("Exponential Distribution")
plt.show()
Relation Between Poisson and Exponential Distributions
- Poisson Distribution: Focuses on the number of events occurring within a fixed time period.
- Exponential Distribution: Focuses on the time between consecutive events.
