rv_histogram — SciPy v1.15.2 Manual (original) (raw)

scipy.stats.

class scipy.stats.rv_histogram(histogram, *args, density=None, **kwargs)[source]#

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 of numpy.histogram is accepted.

densitybool, optional

If False, assumes the histogram is proportional to counts per bin; otherwise, assumes it is proportional to a density. For constant bin widths, these are equivalent, but the distinction is important when bin widths vary (see Notes). If None (default), sets density=True for backwards compatibility, but warns if the bin widths are variable. Set density explicitly to silence the warning.

Added in version 1.10.0.

Notes

When a histogram has unequal bin widths, there is a distinction between histograms that are proportional to counts per bin and histograms that are proportional to probability density over a bin. If numpy.histogram is called with its default density=False, the resulting histogram is the number of counts per bin, so density=False should be passed torv_histogram. If numpy.histogram is called with density=True, the resulting histogram is in terms of probability density, so density=Trueshould be passed to rv_histogram. To avoid warnings, always passdensity explicitly when the input histogram has unequal bin widths.

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.

Added 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, density=False)

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) fig, ax = plt.subplots() ax.set_title("PDF from Template") ax.hist(data, density=True, bins=100) ax.plot(X, hist_dist.pdf(X), label='PDF') ax.plot(X, hist_dist.cdf(X), label='CDF') ax.legend() fig.show()

Attributes:

random_state

Get or set the generator object for generating random variates.

Methods