# numpy.random.power¶

numpy.random.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. samples : {ndarray, scalar} The returned samples lie in [0, 1]. ValueError : If a<1.

Notes

The probability density function is 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

 [R207] Christian Kleiber, Samuel Kotz, “Statistical size distributions in economics and actuarial sciences”, Wiley, 2003.
 [R208] 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

Draw samples from the distribution:

```>>> a = 5. # shape
>>> samples = 1000
>>> s = np.random.power(a, samples)
```

Display the histogram of the samples, along with the probability density function:

```>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s, bins=30)
>>> x = np.linspace(0, 1, 100)
>>> y = a*x**(a-1.)
>>> normed_y = samples*np.diff(bins)*y
>>> plt.plot(x, normed_y)
>>> plt.show()
``` Compare the power function distribution to the inverse of the Pareto.

```>>> from scipy import stats
>>> rvs = np.random.power(5, 1000000)
>>> rvsp = np.random.pareto(5, 1000000)
>>> xx = np.linspace(0,1,100)
>>> powpdf = stats.powerlaw.pdf(xx,5)
```
```>>> plt.figure()
>>> plt.hist(rvs, bins=50, normed=True)
>>> plt.plot(xx,powpdf,'r-')
>>> plt.title('np.random.power(5)')
```
```>>> plt.figure()
>>> plt.hist(1./(1.+rvsp), bins=50, normed=True)
>>> plt.plot(xx,powpdf,'r-')
>>> plt.title('inverse of 1 + np.random.pareto(5)')
```
```>>> plt.figure()
>>> plt.hist(1./(1.+rvsp), bins=50, normed=True)
>>> plt.plot(xx,powpdf,'r-')
>>> plt.title('inverse of stats.pareto(5)')
``` (png, pdf) (png, pdf) (png, pdf)

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