numpy.random.zipf#

random.zipf(a,size=None)#

Draw samples from a Zipf distribution.

Samples are drawn from a Zipf distribution with specified parametera > 1.

The Zipf distribution (also known as the zeta distribution) is adiscrete probability distribution that satisfies Zipf’s law: thefrequency of an item is inversely proportional to its rank in afrequency table.

Note

New code should use thezipfmethod of aGenerator instance instead;please see theQuick start.

Parameters:

afloat or array_like of floats

Distribution parameter. Must be greater than 1.

sizeint or tuple of ints, optional

Output shape. If the given shape is, e.g.,(m,n,k), thenm*n*k samples are drawn. If size isNone (default),a single value is returned ifa is a scalar. Otherwise,np.array(a).size samples are drawn.

Returns:

outndarray or scalar

Drawn samples from the parameterized Zipf distribution.

See also

scipy.stats.zipf

probability density function, distribution, or cumulative density function, etc.

random.Generator.zipf

which should be used for new code.

Notes

The probability mass function (PMF) for the Zipf distribution is

\[p(k) = \frac{k^{-a}}{\zeta(a)},\]

for integers\(k \geq 1\), where\(\zeta\) is the Riemann Zetafunction.

It is named for the American linguist George Kingsley Zipf, who notedthat the frequency of any word in a sample of a language is inverselyproportional to its rank in the frequency table.

References

[1]

Zipf, G. K., “Selected Studies of the Principle of RelativeFrequency in Language,” Cambridge, MA: Harvard Univ. Press,1932.

Examples

Try it in your browser!

Draw samples from the distribution:

>>>a=4.0>>>n=20000>>>s=np.random.zipf(a,n)

Display the histogram of the samples, along withthe expected histogram based on the probabilitydensity function:

>>>importmatplotlib.pyplotasplt>>>fromscipy.specialimportzeta

bincount provides a fast histogram for small integers.

>>>count=np.bincount(s)>>>k=np.arange(1,s.max()+1)

>>>plt.bar(k,count[1:],alpha=0.5,label='sample count')>>>plt.plot(k,n*(k**-a)/zeta(a),'k.-',alpha=0.5,...label='expected count')>>>plt.semilogy()>>>plt.grid(alpha=0.4)>>>plt.legend()>>>plt.title(f'Zipf sample, a={a}, size={n}')>>>plt.show()

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