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. 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. extradoc : str, optional This string is used as the last part of the docstring returned when a subclass has no docstring of its own. Note: `extradoc` exists for backwards compatibility, do not use for new subclasses. seed : None, int, `~np.random.RandomState`, `~np.random.Generator`, optional This parameter defines the object to use for drawing random variates. If `seed` is `None` the `~np.random.RandomState` singleton is used. If `seed` is an int, a new ``RandomState`` instance is used, seeded with seed. If `seed` is already a ``RandomState`` or ``Generator`` instance, then that object is used. Default is None.
Methods ------- rvs pmf logpmf cdf logcdf sf logsf ppf isf moment stats entropy expect median mean std var interval __call__ support
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:
- 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``.)
- scale parameter is not defined.
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 ``ProbX=xk = pk`` by using the ``values`` keyword argument to the `rv_discrete` constructor.
Examples --------
Custom made discrete distribution:
>>> 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)