# scipy.stats.powerlaw¶

scipy.stats.powerlaw()

A power-function continuous random variable.

Continuous 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:

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) scale : array-like, optional scale parameter (default=1) size : int or tuple of ints, optional shape of random variates (default computed from input arguments ) moments : string, 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’) powerlaw.rvs(a,loc=0,scale=1,size=1) : random variates powerlaw.pdf(x,a,loc=0,scale=1) : probability density function powerlaw.cdf(x,a,loc=0,scale=1) : cumulative density function powerlaw.sf(x,a,loc=0,scale=1) : survival function (1-cdf — sometimes more accurate) powerlaw.ppf(q,a,loc=0,scale=1) : percent point function (inverse of cdf — percentiles) powerlaw.isf(q,a,loc=0,scale=1) : inverse survival function (inverse of sf) powerlaw.stats(a,loc=0,scale=1,moments=’mv’) : mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’) powerlaw.entropy(a,loc=0,scale=1) : (differential) entropy of the RV. powerlaw.fit(data,a,loc=0,scale=1) : Parameter estimates for powerlaw data Alternatively, the object may be called (as a function) to fix the shape, : location, and scale parameters returning a “frozen” continuous RV object: : rv = powerlaw(a,loc=0,scale=1) : frozen RV object with the same methods but holding the given shape, location, and scale fixed

Examples

```>>> import matplotlib.pyplot as plt
>>> numargs = powerlaw.numargs
>>> [ a ] = [0.9,]*numargs
>>> rv = powerlaw(a)
```

Display frozen pdf

```>>> x = np.linspace(0,np.minimum(rv.dist.b,3))
>>> h=plt.plot(x,rv.pdf(x))
```

Check accuracy of cdf and ppf

```>>> prb = powerlaw.cdf(x,a)
>>> h=plt.semilogy(np.abs(x-powerlaw.ppf(prb,c))+1e-20)
```

Random number generation

```>>> R = powerlaw.rvs(a,size=100)
```

Power-function distribution

powerlaw.pdf(x,a) = a**x**(a-1) for 0 <= x <= 1, a > 0.

#### Previous topic

scipy.stats.pareto

#### Next topic

scipy.stats.powerlognorm