numpy.random.Generator.pareto#

method

random.Generator.pareto(a,size=None)#

Draw samples from a Pareto II (AKA Lomax) distribution withspecified shape.

Parameters:

afloat or array_like of floats

Shape of the distribution. Must be positive.

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 Pareto II distribution.

See also

scipy.stats.pareto

Pareto I distribution

scipy.stats.lomax

Lomax (Pareto II) distribution

scipy.stats.genpareto

Generalized Pareto distribution

Notes

The probability density for the Pareto II distribution is

\[p(x) = \frac{a}{(x+1)^{a+1}} , x \ge 0\]

where\(a > 0\) is the shape.

The Pareto II distribution is a shifted and scaled version of thePareto I distribution, which can be found inscipy.stats.pareto.

References

[1]

Francis Hunt and Paul Johnson, On the Pareto Distribution ofSourceforge projects.

[2]

Pareto, V. (1896). Course of Political Economy. Lausanne.

[3]

Reiss, R.D., Thomas, M.(2001), Statistical Analysis of ExtremeValues, Birkhauser Verlag, Basel, pp 23-30.

[4]

Wikipedia, “Pareto distribution”,https://en.wikipedia.org/wiki/Pareto_distribution

Examples

Try it in your browser!

Draw samples from the distribution:

>>>a=3.>>>rng=np.random.default_rng()>>>s=rng.pareto(a,10000)

Display the histogram of the samples, along with the probabilitydensity function:

>>>importmatplotlib.pyplotasplt>>>x=np.linspace(0,3,50)>>>pdf=a/(x+1)**(a+1)>>>plt.hist(s,bins=x,density=True,label='histogram')>>>plt.plot(x,pdf,linewidth=2,color='r',label='pdf')>>>plt.xlim(x.min(),x.max())>>>plt.legend()>>>plt.show()

Go BackOpen In Tab