scipy.stats.zipf

scipy.stats.zipf = <scipy.stats._discrete_distns.zipf_gen object at 0x7fe7c49ec278>

A Zipf 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:

scipy.stats.rvs(a, loc=0, size=1)

Random variates.

scipy.stats.pmf(x, a, loc=0)

Probability mass function.

scipy.stats.logpmf(x, a, loc=0)

Log of the probability mass function.

scipy.stats.cdf(x, a, loc=0)

Cumulative density function.

scipy.stats.logcdf(x, a, loc=0)

Log of the cumulative density function.

scipy.stats.sf(x, a, loc=0)

Survival function (1-cdf --- sometimes more accurate).

scipy.stats.logsf(x, a, loc=0)

Log of the survival function.

scipy.stats.ppf(q, a, loc=0)

Percent point function (inverse of cdf --- percentiles).

scipy.stats.isf(q, a, loc=0)

Inverse survival function (inverse of sf).

scipy.stats.stats(a, loc=0, moments='mv')

Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').

scipy.stats.entropy(a, loc=0)

(Differential) entropy of the RV.

scipy.stats.expect(func, a, loc=0, lb=None, ub=None, conditional=False)

Expected value of a function (of one argument) with respect to the distribution.

scipy.stats.median(a, loc=0)

Median of the distribution.

scipy.stats.mean(a, loc=0)

Mean of the distribution.

scipy.stats.var(a, loc=0)

Variance of the distribution.

scipy.stats.std(a, loc=0)

Standard deviation of the distribution.

scipy.stats.interval(alpha, a, loc=0)

Endpoints of the range that contains alpha percent of the distribution

Parameters:

• x (array_like) -- quantiles
• q (array_like) -- lower or upper tail probability
• a (array_like) -- shape parameters
• loc (array_like, optional) -- location parameter (default=0)
• size (int or tuple of ints, optional) -- shape of random variates (default computed from input arguments )
• moments (str, optional) -- composed of letters ['mvsk'] specifying which moments to compute where 'm' = mean, 'v' = variance, 's' = (Fisher's) skew and 'k' = (Fisher's) kurtosis. (default='mv')
• the object may be called (as a function) to fix the shape and (Alternatively,) --
• parameters returning a "frozen" discrete RV object (location) --
• = zipf(a, loc=0) (rv) --
  • Frozen RV object with the same methods but holding the given shape and

  location fixed.

Notes

The probability mass function for zipf is:

zipf.pmf(k, a) = 1/(zeta(a) * k**a)

for k >= 1.

zipf takes a as shape parameter.

Examples

>>> from scipy.stats import zipf
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)

Calculate a few first moments:

>>> a = 6.5
>>> mean, var, skew, kurt = zipf.stats(a, moments='mvsk')

Display the probability mass function (pmf):

>>> x = np.arange(zipf.ppf(0.01, a),
...               zipf.ppf(0.99, a))
>>> ax.plot(x, zipf.pmf(x, a), 'bo', ms=8, label='zipf pmf')
>>> ax.vlines(x, 0, zipf.pmf(x, a), colors='b', lw=5, alpha=0.5)

Alternatively, freeze the distribution and display the frozen pmf:

>>> rv = zipf(a)
>>> ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1,
...         label='frozen pmf')
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

Check accuracy of cdf and ppf:

>>> prob = zipf.cdf(x, a)
>>> np.allclose(x, zipf.ppf(prob, a))
True

Generate random numbers:

>>> r = zipf.rvs(a, size=1000)