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scipy.stats.

# rv_histogram

class scipy.stats.rv_histogram(histogram, *args, density=None, **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 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.

  Attributes:
    `random_state`

      Get or set the generator 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 estimates of 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`(confidence, *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`(order, *args, **kwds) | non-central moment of distribution of specified order.
  `nnlf`(theta, x) | 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) | Support of the distribution.
  `var`(*args, **kwds) | Variance of the distribution.

  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 to `rv_histogram`. If `numpy.histogram` is called with `density=True`, the resulting histogram is in terms of probability density, so `density=True` should be passed to `rv_histogram`. To avoid warnings, always pass `density` 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()