numpy.random.mtrand.RandomState.power¶

RandomState.power(a, size=None)¶

Draws samples in [0, 1] from a power distribution with positive exponent a - 1.

Also known as the power function distribution.

Parameters:

a : float

parameter, > 0

size : tuple of ints

Output shape. If the given shape is, e.g., (m, n, k), then

m * n * k samples are drawn.

Returns:

samples : {ndarray, scalar}

The returned samples lie in [0, 1].

Raises:

ValueError :

If a<1.

Notes

The probability density function is

$P(x; a) = ax^{a-1}, 0 \le x \le 1, a>0.$

The power function distribution is just the inverse of the Pareto distribution. It may also be seen as a special case of the Beta distribution.

It is used, for example, in modeling the over-reporting of insurance claims.

References

Christian Kleiber, Samuel Kotz, “Statistical size distributions in economics and actuarial sciences”, Wiley, 2003.

Heckert, N. A. and Filliben, James J. (2003). NIST Handbook 148: Dataplot Reference Manual, Volume 2: Let Subcommands and Library Functions”, National Institute of Standards and Technology Handbook Series, June 2003. http://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf

Examples