Exponential Distribution in NumPy (original) (raw)

Last Updated : 10 Dec, 2025

The Exponential Distribution is a continuous probability distribution that describes the time between two events in a Poisson process, where events occur independently and at a constant average rate. NumPy provides a simple method to generate such random values: numpy.random.exponential().

**Example: This example shows how to generate one exponential random value using the default parameters.

Python `

import numpy as np x = np.random.exponential() print(x)

`

**Explanation:

• np.random.exponential() generates one value following the exponential distribution.
• Since no parameters are passed, it uses scale = 1 by default.

Syntax

numpy.random.exponential(scale=1.0, size=None)

**Parameters:

• **scale: Inverse of the event rate (β = 1/λ).
• **size: Shape of output array.

Examples

**Example 1: This example generates one exponential random value using a custom scale.

Python `

import numpy as np x = np.random.exponential(scale=2) print(x)

`

**Explanation:

• scale=2 values will be more spread out.
• x holds a single exponential random number.
• Larger scale values make the distribution longer and wider.

**Example 2: This example generates five random numbers from the exponential distribution.

Python `

import numpy as np arr = np.random.exponential(scale=1.5, size=5) print(arr)

`

Output

[2.14106221 1.93254045 0.03957526 0.58763751 1.12814399]

**Explanation

• scale=1.5 moderate spread.
• size=5 returns 5 values.
• arr stores the array like [0.21, 1.33, 0.94, ...].

Visualizing the Exponential Distribution

Visualizing the generated numbers helps in understanding their behavior. Below is an example of plotting a histogram of random numbers generated using numpy.random.exponential.

Python `

import numpy as np import matplotlib.pyplot as plt import seaborn as sns

s = 2 # scale n = 800 # number of points

data = np.random.exponential(scale=s, size=n) sns.histplot(data, bins=30, kde=True, edgecolor='black')

plt.title(f"Exponential Distribution (Scale={s})") plt.xlabel("Value") plt.ylabel("Frequency") plt.grid(True) plt.show()

`

**Output

Exponenetial Distribution Plot

**Explanation:

• s = 2 sets the spread of the distribution.
• n = 800 creates enough data points for a smooth histogram.
• sns.histplot() shows: Bars -> simulated data and Curve (kde) -> smooth theoretical shape
• The graph shows high frequency near 0 and a long decreasing tail, which is typical of exponential distributions.