Overflow error subclassing a distribution using scipy.stats.rv_continuous - python-3.x

Question

In the documentation page of rv_continuous we can find a 'custom' gaussian being subclassed as follows.
from scipy.stats import rv_continuous
import numpy as np
class gaussian_gen(rv_continuous):
"Gaussian distribution"
def _pdf(self, x):
return np.exp(-x**2 / 2.) / np.sqrt(2.0 * np.pi)
gaussian = gaussian_gen(name='gaussian')
In turn, I attempted to create a class for an exponential distribution with base 2, to model some nuclear decay:
class time_dist(rv_continuous):
def _pdf(self, x):
return 2**(-x)
random_var = time_dist(name = 'decay')
This had the purpose of then calling random_var.rvs() in order to generate a randomly distributed sample of values according to the pdf I defined. However, when I run this, I receive an OverflowError, and I don't quite understand why. Initially I thought it had to do with the fact that the function was not normalized. However, I keep making changes to the _pdf definition to no avail. Is there anything wrong with the code or is this method just ill-advised for defining functions of this sort?

Answer 1

According to wikipedia, the pdf of an exponential distribution would be:
lambda * exp(-lambda*x) for x >= 0
0 for x < 0
So, probably the function should be changed as follows:
from scipy.stats import rv_continuous
import numpy as np
import matplotlib.pyplot as plt
class time_dist(rv_continuous):
def _pdf(self, x):
return np.log(2) * 2 ** (-x) if x >= 0 else 0
random_var = time_dist(name='decay')
plt.hist(random_var.rvs(size=500))
plt.show()