# scipy.stats.pareto¶

scipy.stats.pareto()

A Pareto 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 b : 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’) pareto.rvs(b,loc=0,scale=1,size=1) : random variates pareto.pdf(x,b,loc=0,scale=1) : probability density function pareto.cdf(x,b,loc=0,scale=1) : cumulative density function pareto.sf(x,b,loc=0,scale=1) : survival function (1-cdf — sometimes more accurate) pareto.ppf(q,b,loc=0,scale=1) : percent point function (inverse of cdf — percentiles) pareto.isf(q,b,loc=0,scale=1) : inverse survival function (inverse of sf) pareto.stats(b,loc=0,scale=1,moments=’mv’) : mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’) pareto.entropy(b,loc=0,scale=1) : (differential) entropy of the RV. pareto.fit(data,b,loc=0,scale=1) : Parameter estimates for pareto 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 = pareto(b,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 = pareto.numargs
>>> [ b ] = [0.9,]*numargs
>>> rv = pareto(b)
```

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

Random number generation

```>>> R = pareto.rvs(b,size=100)
```

Pareto distribution

pareto.pdf(x,b) = b/x**(b+1) for x >= 1, b > 0.

scipy.stats.nct

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scipy.stats.powerlaw