# scipy.stats.cauchy¶

scipy.stats.cauchy()

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

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 = cauchy.cdf(x,<shape(s)>)
>>> h=plt.semilogy(np.abs(x-cauchy.ppf(prb,c))+1e-20)
```

Random number generation

```>>> R = cauchy.rvs(size=100)
```

Cauchy distribution

cauchy.pdf(x) = 1/(pi*(1+x**2))

This is the t distribution with one degree of freedom.

scipy.stats.fisk

scipy.stats.chi