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The probability density function for this class is:

for a \le x \le b, b > a > 0. This class takes a and b as shape parameters.

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%(example)s

This doesn't show the equal probability of 0.01, 0.1 and 1. This is best when the x-axis is log-scaled:

>>> import numpy as np
>>> fig, ax = plt.subplots(1, 1)
>>> ax.hist(np.log10(r))
>>> ax.set_ylabel("Frequency")
>>> ax.set_xlabel("Value of random variable")
>>> ax.xaxis.set_major_locator(plt.FixedLocator([-2, -1, 0]))
>>> ticks = ["$10^{{ {} }}$".format(i) for i in [-2, -1, 0]]
>>> ax.set_xticklabels(ticks)  # doctest: +SKIP
>>> plt.show()

This random variable will be log-uniform regardless of the base chosen for a and b. Let's specify with base 2 instead:

>>> rvs = %(name)s(2**-2, 2**0).rvs(size=1000)

Values of 1/4, 1/2 and 1 are equally likely with this random variable. Here's the histogram:

>>> fig, ax = plt.subplots(1, 1)
>>> ax.hist(np.log2(rvs))
>>> ax.set_ylabel("Frequency")
>>> ax.set_xlabel("Value of random variable")
>>> ax.xaxis.set_major_locator(plt.FixedLocator([-2, -1, 0]))
>>> ticks = ["$2^{{ {} }}$".format(i) for i in [-2, -1, 0]]
>>> ax.set_xticklabels(ticks)  # doctest: +SKIP
>>> plt.show()

A loguniform or reciprocal continuous random variable.