scipy.stats._distn_infrastructure:rv_discrete

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.