.exponential()

The .exponential() function in NumPy random module generates random numbers from an exponential distribution, where the scale parameter (1/λ) controls the spread, and the size defines the shape of the output array.

Syntax

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

Parameters:

• scale (float, optional): The scale parameter (β = 1/λ) is also the distribution’s mean. Must be > 0. The default is 1.0.
• size (int or tuple of ints, optional): Output shape. If None (default), returns a single value. If an integer or tuple, returns an array of that shape.

Return value:

It returns random samples from the exponential distribution.

Its probability density function is:

$f(x; \frac{1}{\beta}) = \frac{1}{\beta} \exp(-\frac{x}{\beta}),$

Here, $\beta$ is the scale parameter (also the mean), and $\lambda = 1/\beta$ is the rate. This is a standard parameterization of the exponential distribution.

Example

The following code returns 10 random samples from an exponential distribution with a scale of 0.75. Setting the seed ensures reproducible results:

import numpy as np
np.random.seed(23)
results = np.random.exponential(scale=0.75, size=10)
print(results)

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The output of this code will be:

[0.54626666 2.20256852 1.08759608 0.24887788 0.18735185 0.86930237 0.13716657 0.3737313  0.72185379 0.39818209]

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Codebyte Example

In this example, the waiting times between 100 calls to a help desk are simulated, where calls arrive randomly but on average every 5 minutes:

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Here:

• scale=5.0 means the average time between calls is 5 minutes.
• size=100 generates 100 waiting time values.
• np.random.exponential(...) creates the random samples from an exponential distribution.
• Only the first 10 values are printed for brevity.

This example demonstrates how exponential distribution can be used to model real-world scenarios like time intervals between incoming events.