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 or int or ``numpy.random.RandomState`` instance, optional This parameter defines the RandomState object to use for drawing random variates. If None, the global np.random state is used. If integer, it is used to seed the local RandomState instance. 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)