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 c : 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 : str, 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’) Alternatively, the object may be called (as a function) to fix the shape, location, and scale parameters returning a “frozen” continuous RV object: rv = bradford(c, loc=0, scale=1) Frozen RV object with the same methods but holding the given shape, location, and scale fixed.

Notes

The probability density function for bradford is:

bradford.pdf(x, c) = c / (k * (1+c*x)),

for 0 < x < 1, c > 0 and k = log(1+c).

Examples

>>> [ c ] = [0.9,] * numargs

Display frozen pdf

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

Here, rv.dist.b is the right endpoint of the support of rv.dist.

Check accuracy of cdf and ppf

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

Random number generation