>>> import numpy as np
>>> from scipy.stats import loguniform
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)
Calculate the first four moments:
>>> a, b = 0.01, 1.25
>>> mean, var, skew, kurt = loguniform.stats(a, b, moments='mvsk')
Display the probability density function (pdf
):
>>> x = np.linspace(loguniform.ppf(0.01, a, b),
... loguniform.ppf(0.99, a, b), 100)
>>> ax.plot(x, loguniform.pdf(x, a, b),
... 'r-', lw=5, alpha=0.6, label='loguniform pdf')
Alternatively, the distribution object can be called (as a function)
to fix the shape, location and scale parameters. This returns a “frozen”
RV object holding the given parameters fixed.
Freeze the distribution and display the frozen pdf
:
>>> rv = loguniform(a, b)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of cdf
and ppf
:
>>> vals = loguniform.ppf([0.001, 0.5, 0.999], a, b)
>>> np.allclose([0.001, 0.5, 0.999], loguniform.cdf(vals, a, b))
Generate random numbers:
>>> r = loguniform.rvs(a, b, size=1000)
And compare the histogram:
>>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
>>> ax.set_xlim([x[0], x[-1]])
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()
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
>>> import matplotlib.pyplot as plt
>>> 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)
>>> 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 = loguniform(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)
>>> plt.show()
sf(x, a, b, loc=0, scale=1)
Survival function (also defined as 1 - cdf
, but sf is sometimes more accurate).
logsf(x, a, b, loc=0, scale=1)
Log of the survival function.
ppf(q, a, b, loc=0, scale=1)
Percent point function (inverse of cdf
— percentiles).
isf(q, a, b, loc=0, scale=1)
Inverse survival function (inverse of sf
).
moment(order, a, b, loc=0, scale=1)
Non-central moment of the specified order.
stats(a, b, loc=0, scale=1, moments=’mv’)
Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(a, b, loc=0, scale=1)
(Differential) entropy of the RV.
fit(data)
Parameter estimates for generic data. See scipy.stats.rv_continuous.fit for detailed documentation of the keyword arguments.
expect(func, args=(a, b), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)
Expected value of a function (of one argument) with respect to the distribution.
median(a, b, loc=0, scale=1)
Median of the distribution.
mean(a, b, loc=0, scale=1)
Mean of the distribution.
var(a, b, loc=0, scale=1)
Variance of the distribution.
std(a, b, loc=0, scale=1)
Standard deviation of the distribution.
interval(confidence, a, b, loc=0, scale=1)
Confidence interval with equal areas around the median.