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# scipy.stats.rv_discrete

class scipy.stats.rv_discrete(a=0, b=inf, name=None, badvalue=None, moment_tol=1e-08, values=None, inc=1, longname=None, shapes=None, seed=None)

  A generic discrete random variable class meant for subclassing.

  `rv_discrete` is a base class to construct specific distribution classes and instances for discrete random variables. It can also be used to construct an arbitrary distribution defined by a list of support points and corresponding probabilities.

  Parameters:
    a float, optional

      Lower bound of the support of the distribution, default: 0

    b float, optional

      Upper bound of the support of the distribution, default: plus infinity

    moment_tol float, optional

      The tolerance for the generic calculation of moments.

    values tuple of two array_like, optional

      `(xk, pk)` where `xk` are integers and `pk` are the non-zero probabilities between 0 and 1 with `sum(pk) = 1`. `xk` and `pk` must have the same shape, and `xk` must be unique.

    inc integer, optional

      Increment for the support of the distribution. Default is 1. (other values have not been tested)

    badvalue float, optional

      The value in a result arrays that indicates a value that for which some argument restriction is violated, default is np.nan.

    name str, optional

      The name of the instance. This string is used to construct the default example for distributions.

    longname str, optional

      This string is used as part of the first line of the docstring returned when a subclass has no docstring of its own. Note: longname exists for backwards compatibility, do not use for new subclasses.

    shapes str, optional

      The shape of the distribution. For example “m, n” for a distribution that takes two integers as the two shape arguments for all its methods If not provided, shape parameters will be inferred from the signatures of the private methods, `_pmf` and `_cdf` of the instance.

    seed{None, int, `numpy.random.Generator`, `numpy.random.RandomState`}, optional

      If seed is None (or np.random), the `numpy.random.RandomState` singleton is used. If seed is an int, a new `RandomState` instance is used, seeded with seed. If seed is already a `Generator` or `RandomState` instance then that instance is used.

  Notes

  This class is similar to `rv_continuous`. Whether a shape parameter is valid is decided by an `_argcheck` method (which defaults to checking that its arguments are strictly positive.) The main differences are as follows.

  - The support of the distribution is a set of integers.

  - Instead of the probability density function, `pdf` (and the corresponding private `_pdf`), this class defines the probability mass function, `pmf` (and the corresponding private `_pmf`.)

  - There is no `scale` parameter.

  - The default implementations of methods (e.g. `_cdf`) are not designed for distributions with support that is unbounded below (i.e. `a=-np.inf`), so they must be overridden.

  To create a new discrete distribution, we would do the following:

      >>> from scipy.stats import rv_discrete
      >>> class poisson_gen(rv_discrete):
      ...     "Poisson distribution"
      ...     def _pmf(self, k, mu):
      ...         return exp(-mu) * mu**k / factorial(k)

  and create an instance:

      >>> poisson = poisson_gen(name="poisson")

  Note that above we defined the Poisson distribution in the standard form. Shifting the distribution can be done by providing the `loc` parameter to the methods of the instance. For example, `poisson.pmf(x, mu, loc)` delegates the work to `poisson._pmf(x-loc, mu)`.

  Discrete distributions from a list of probabilities

  Alternatively, you can construct an arbitrary discrete rv defined on a finite set of values `xk` with `Prob{X=xk} = pk` by using the `values` keyword argument to the `rv_discrete` constructor.

  Deepcopying / Pickling

  If a distribution or frozen distribution is deepcopied (pickled/unpickled, etc.), any underlying random number generator is deepcopied with it. An implication is that if a distribution relies on the singleton RandomState before copying, it will rely on a copy of that random state after copying, and `np.random.seed` will no longer control the state.

  Examples

  Custom made discrete distribution:

      >>> import numpy as np
      >>> from scipy import stats
      >>> xk = np.arange(7)
      >>> pk = (0.1, 0.2, 0.3, 0.1, 0.1, 0.0, 0.2)
      >>> custm = stats.rv_discrete(name='custm', values=(xk, pk))
      >>>
      >>> import matplotlib.pyplot as plt
      >>> fig, ax = plt.subplots(1, 1)
      >>> ax.plot(xk, custm.pmf(xk), 'ro', ms=12, mec='r')
      >>> ax.vlines(xk, 0, custm.pmf(xk), colors='r', lw=4)
      >>> plt.show()

  Random number generation:

      >>> R = custm.rvs(size=100)

  Attributes:
    `random_state`

      Get or set the generator object for generating random variates.

  Methods

  `rvs`(*args, **kwargs) | Random variates of given type.
  `pmf`(k, *args, **kwds) | Probability mass function at k of the given RV.
  `logpmf`(k, *args, **kwds) | Log of the probability mass function at k of the given RV.
  `cdf`(k, *args, **kwds) | Cumulative distribution function of the given RV.
  `logcdf`(k, *args, **kwds) | Log of the cumulative distribution function at k of the given RV.
  `sf`(k, *args, **kwds) | Survival function (1 - `cdf`) at k of the given RV.
  `logsf`(k, *args, **kwds) | Log of the survival function of the given RV.
  `ppf`(q, *args, **kwds) | Percent point function (inverse of `cdf`) at q of the given RV.
  `isf`(q, *args, **kwds) | Inverse survival function (inverse of `sf`) at q of the given RV.
  `moment`(order, *args, **kwds) | non-central moment of distribution of specified order.
  `stats`(*args, **kwds) | Some statistics of the given RV.
  `entropy`(*args, **kwds) | Differential entropy of the RV.
  `expect`([func, args, loc, lb, ub, ...]) | Calculate expected value of a function with respect to the distribution for discrete distribution by numerical summation.
  `median`(*args, **kwds) | Median of the distribution.
  `mean`(*args, **kwds) | Mean of the distribution.
  `std`(*args, **kwds) | Standard deviation of the distribution.
  `var`(*args, **kwds) | Variance of the distribution.
  `interval`(confidence, *args, **kwds) | Confidence interval with equal areas around the median.
  `__call__`(*args, **kwds) | Freeze the distribution for the given arguments.
  `support`(*args, **kwargs) | Support of the distribution.