ENH: improve accuracy of ppf cdf roundtrip for gumbel_l

[pbrod]

The accuracy of the gumbel_l ppf and cdf functions is poor for large negative x as exemplified here:

>>> import numpy as np
>>> import scipy.stats as ss
>>> x = np.linspace(-100, -4)
>>> (ss.gumbel_l.ppf(ss.gumbel_l.cdf(x))-x)/x
array([             inf,              inf,              inf,
                inf,              inf,              inf,
                inf,              inf,              inf,
                inf,              inf,              inf,
                inf,              inf,              inf,
                inf,              inf,              inf,
                inf,              inf,              inf,
                inf,              inf,              inf,
                inf,              inf,              inf,
                inf,              inf,              inf,
                inf,              inf,  -1.52608162e-02,
     1.00926224e-04,   5.04405205e-04,  -1.22679122e-06,
    -3.82136386e-06,  -3.94631612e-07,  -5.56583419e-08,
    -9.00121598e-09,   3.31592421e-09,   4.64076847e-10,
    -7.81227413e-11,  -1.62509384e-11,  -2.56347474e-12,
     2.74780964e-13,  -9.17172674e-14,  -1.17775205e-14,
     2.68278550e-15,   6.66133815e-16])

By replacing the _cdf and _ppf methods with

def _cdf(self, x):
    return -expm1(-exp(x))

def _ppf(self, q):
    return log(-log1p(-q))

one will obtain full machine accuracy as shown here:

>>> (ss.gumbel_l.ppf(ss.gumbel_l.cdf(x))-x)/x
array([-0., -0., -0., -0., -0., -0., -0., -0., -0., -0., -0., -0., -0.,
         -0., -0., -0., -0., -0., -0., -0., -0., -0., -0., -0., -0., -0.,
         -0., -0., -0., -0., -0., -0., -0., -0., -0., -0., -0., -0., -0.,
         -0., -0., -0., -0., -0., -0., -0., -0., -0., -0., -0.])

One should also consider replacing the _logsf and _sf methods with

def _logsf(self, x):
    return -exp(x)

def _sf(self, x):
    return exp(-exp(x))

in order to improve the accuracy for those methods as well.

[rgommers]

Thanks @pbrod, nice set of related improvements in this and other recent issues!

[pbrod]

Thanks.