"""Log-laplace distribution."""
import numpy
from scipy import special, misc
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class log_laplace(SimpleDistribution):
"""Log-laplace distribution."""
def __init__(self, c):
super(log_laplace, self).__init__(dict(c=c))
def _pdf(self, x, c):
cd2 = c / 2.0
c = numpy.where(x < 1, c, -c)
return cd2 * x ** (c - 1)
def _cdf(self, x, c):
return numpy.where(x < 1, 0.5 * x**c, 1 - 0.5 * x ** (-c))
def _ppf(self, q, c):
return numpy.where(
q < 0.5, (2.0 * q) ** (1.0 / c), (2 * (1.0 - q)) ** (-1.0 / c)
)
def _lower(self, c):
return 0.0
def _upper(self, c):
return 2e12 ** (1.0 / c)
[docs]class LogLaplace(ShiftScaleDistribution):
"""
Log-laplace distribution
Args:
shape (float, Distribution):
Shape parameter
scale (float, Distribution):
Scaling parameter
shift (float, Distribution):
Location parameter
Examples:
>>> distribution = chaospy.LogLaplace(5)
>>> distribution
LogLaplace(5)
>>> uloc = numpy.linspace(0, 1, 6)
>>> uloc
array([0. , 0.2, 0.4, 0.6, 0.8, 1. ])
>>> xloc = distribution.inv(uloc)
>>> xloc.round(3)
array([ 0. , 0.833, 0.956, 1.046, 1.201, 288.54 ])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0. , 1.201, 2.091, 1.913, 0.833, 0. ])
>>> distribution.sample(4).round(3)
array([1.076, 0.745, 1.587, 0.993])
"""
[docs] def __init__(self, shape=1, scale=1, shift=0):
super(LogLaplace, self).__init__(
dist=log_laplace(shape),
scale=scale,
shift=shift,
repr_args=[shape],
)