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, extradoc=None)

A Generic discrete random variable.

Discrete random variables are defined from a standard form and may require some shape parameters to complete its specification. Any optional keyword parameters can be passed to the methods of the RV object as given below:


generic.rvs(<shape(s)>,loc=0,size=1) :

  • random variates

generic.pmf(x,<shape(s)>,loc=0) :

  • probability mass function

generic.cdf(x,<shape(s)>,loc=0) :

  • cumulative density function

generic.sf(x,<shape(s)>,loc=0) :

  • survival function (1-cdf — sometimes more accurate)

generic.ppf(q,<shape(s)>,loc=0) :

  • percent point function (inverse of cdf — percentiles)

generic.isf(q,<shape(s)>,loc=0) :

  • inverse survival function (inverse of sf)

generic.stats(<shape(s)>,loc=0,moments=’mv’) :

  • mean(‘m’,axis=0), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’)

generic.entropy(<shape(s)>,loc=0) :

  • entropy of the RV

Alternatively, the object may be called (as a function) to fix :

the shape and location parameters returning a :

“frozen” discrete RV object: :

myrv = generic(<shape(s)>,loc=0) :

  • frozen RV object with the same methods but holding the given shape and location fixed.

You can construct an aribtrary discrete rv where P{X=xk} = pk :

by passing to the rv_discrete initialization method (through the values= :

keyword) a tuple of sequences (xk,pk) which describes only those values of :

X (xk) that occur with nonzero probability (pk). :


>>> import matplotlib.pyplot as plt
>>> numargs = generic.numargs
>>> [ <shape(s)> ] = ['Replace with resonable value',]*numargs

Display frozen pmf:

>>> rv = generic(<shape(s)>)
>>> x = np.arange(0,np.min(rv.dist.b,3)+1)
>>> h = plt.plot(x,rv.pmf(x))

Check accuracy of cdf and ppf:

>>> prb = generic.cdf(x,<shape(s)>)
>>> h = plt.semilogy(np.abs(x-generic.ppf(prb,<shape(s)>))+1e-20)

Random number generation:

>>> R = generic.rvs(<shape(s)>,size=100)

Custom made discrete distribution:

>>> vals = [arange(7),(0.1,0.2,0.3,0.1,0.1,0.1,0.1)]
>>> custm = rv_discrete(name='custm',values=vals)
>>> h = plt.plot(vals[0],custm.pmf(vals[0]))

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