`numpy.random._generator:Generator.exponential`

Signature

def exponential(scale = 1.0, size = None)

Summary

Draw samples from an exponential distribution.

Extended Summary

Its probability density function is

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

for x > 0 and 0 elsewhere. $β$ is the scale parameter, which is the inverse of the rate parameter $λ = 1/ β$ . The rate parameter is an alternative, widely used parameterization of the exponential distribution ^[3].

The exponential distribution is a continuous analogue of the geometric distribution. It describes many common situations, such as the size of raindrops measured over many rainstorms ^[1], or the time between page requests to Wikipedia ^[2].

Parameters

scale : float or array_like of floats: The scale parameter, $β = 1/ λ$ . Must be non-negative.
size : int or tuple of ints, optional: Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. If size is None (default), a single value is returned if scale is a scalar. Otherwise, np.array(scale).size samples are drawn.

Returns

out : ndarray or scalar: Drawn samples from the parameterized exponential distribution.

Examples

Assume a company has 10000 customer support agents and the time between customer calls is exponentially distributed and that the average time between customer calls is 4 minutes.

scale, size = 4, 10000
rng = np.random.default_rng()
time_between_calls = rng.exponential(scale=scale, size=size)

✓

What is the probability that a customer will call in the next 4 to 5 minutes?

x = ((time_between_calls < 5).sum())/size
y = ((time_between_calls < 4).sum())/size

✓

x - y

✗

np.float64(0.08289999999999997)

The corresponding distribution can be visualized as follows:

import matplotlib.pyplot as plt
scale, size = 4, 10000
rng = np.random.default_rng()
sample = rng.exponential(scale=scale, size=size)
count, bins, _ = plt.hist(sample, 30, density=True)

✓

plt.plot(bins, scale**(-1)*np.exp(-scale**-1*bins), linewidth=2, color='r')

✗

[<matplotlib.lines.Line2D object at 0x7f2201771a90>]

plt.show()

✓