# 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, 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:

Methods: generic.rvs(,loc=0,size=1) : random variates generic.pmf(x,,loc=0) : probability mass function generic.cdf(x,,loc=0) : cumulative density function generic.sf(x,,loc=0) : survival function (1-cdf — sometimes more accurate) generic.ppf(q,,loc=0) : percent point function (inverse of cdf — percentiles) generic.isf(q,,loc=0) : inverse survival function (inverse of sf) generic.stats(,loc=0,moments=’mv’) : mean(‘m’,axis=0), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’) generic.entropy(,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(,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). :

Examples

```>>> 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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