scipy.stats.rv_histogram

class scipy.stats.rv_histogram(histogram, *args, **kwargs)

Generates a distribution given by a histogram. This is useful to generate a template distribution from a binned datasample.

As a subclass of the rv_continuous class, rv_histogram inherits from it a collection of generic methods (see rv_continuous for the full list), and implements them based on the properties of the provided binned datasample.

Parameters

histogramtuple of array_like

Tuple containing two array_like objects The first containing the content of n bins The second containing the (n+1) bin boundaries In particular the return value np.histogram is accepted

Notes

There are no additional shape parameters except for the loc and scale. The pdf is defined as a stepwise function from the provided histogram The cdf is a linear interpolation of the pdf.

New in version 0.19.0.

Examples

Create a scipy.stats distribution from a numpy histogram

>>> import scipy.stats
>>> import numpy as np
>>> data = scipy.stats.norm.rvs(size=100000, loc=0, scale=1.5, random_state=123)
>>> hist = np.histogram(data, bins=100)
>>> hist_dist = scipy.stats.rv_histogram(hist)

Behaves like an ordinary scipy rv_continuous distribution

>>> hist_dist.pdf(1.0)
0.20538577847618705
>>> hist_dist.cdf(2.0)
0.90818568543056499

PDF is zero above (below) the highest (lowest) bin of the histogram, defined by the max (min) of the original dataset

>>> hist_dist.pdf(np.max(data))
0.0
>>> hist_dist.cdf(np.max(data))
1.0
>>> hist_dist.pdf(np.min(data))
7.7591907244498314e-05
>>> hist_dist.cdf(np.min(data))
0.0

PDF and CDF follow the histogram

>>> import matplotlib.pyplot as plt
>>> X = np.linspace(-5.0, 5.0, 100)
>>> plt.title("PDF from Template")
>>> plt.hist(data, density=True, bins=100)
>>> plt.plot(X, hist_dist.pdf(X), label='PDF')
>>> plt.plot(X, hist_dist.cdf(X), label='CDF')
>>> plt.show()

Attributes

random_state

Get or set the RandomState object for generating random variates.

Methods

__call__(*args, **kwds)	Freeze the distribution for the given arguments.
cdf(x, *args, **kwds)	Cumulative distribution function of the given RV.
entropy(*args, **kwds)	Differential entropy of the RV.
expect([func, args, loc, scale, lb, ub, …])	Calculate expected value of a function with respect to the distribution by numerical integration.
fit(data, *args, **kwds)	Return MLEs for shape (if applicable), location, and scale parameters from data.
fit_loc_scale(data, *args)	Estimate loc and scale parameters from data using 1st and 2nd moments.
freeze(*args, **kwds)	Freeze the distribution for the given arguments.
interval(alpha, *args, **kwds)	Confidence interval with equal areas around the median.
isf(q, *args, **kwds)	Inverse survival function (inverse of sf) at q of the given RV.
logcdf(x, *args, **kwds)	Log of the cumulative distribution function at x of the given RV.
logpdf(x, *args, **kwds)	Log of the probability density function at x of the given RV.
logsf(x, *args, **kwds)	Log of the survival function of the given RV.
mean(*args, **kwds)	Mean of the distribution.
median(*args, **kwds)	Median of the distribution.
moment(n, *args, **kwds)	n-th order non-central moment of distribution.
nnlf(theta, x)	Return negative loglikelihood function.
pdf(x, *args, **kwds)	Probability density function at x of the given RV.
ppf(q, *args, **kwds)	Percent point function (inverse of cdf) at q of the given RV.
rvs(*args, **kwds)	Random variates of given type.
sf(x, *args, **kwds)	Survival function (1 - cdf) at x of the given RV.
stats(*args, **kwds)	Some statistics of the given RV.
std(*args, **kwds)	Standard deviation of the distribution.
support(*args, **kwargs)	Return the support of the distribution.
var(*args, **kwds)	Variance of the distribution.