"""Hyperbolic secant distribution."""
import numpy
from scipy import special
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class hyperbolic_secant(SimpleDistribution):
"""Hyperbolic secant distribution."""
def __init__(self):
super(hyperbolic_secant, self).__init__()
def _pdf(self, x):
return 0.5 * numpy.cosh(numpy.pi * x / 2.0) ** -1
def _cdf(self, x):
return 2 / numpy.pi * numpy.arctan(numpy.e ** (numpy.pi * x / 2.0))
def _ppf(self, q):
return 2 / numpy.pi * numpy.log(numpy.tan(numpy.pi * q / 2.0))
def _lower(self):
return -21.7
def _upper(self):
return 21.7
def _mom(self, k):
return numpy.abs(special.euler(k.item())[-1])
[docs]class HyperbolicSecant(ShiftScaleDistribution):
"""
Hyperbolic secant distribution
Args:
scale (float, Distribution):
Scale parameter
shift (float, Distribution):
Location parameter
Examples:
>>> distribution = chaospy.HyperbolicSecant()
>>> distribution
HyperbolicSecant()
>>> 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([-21.7 , -0.716, -0.203, 0.203, 0.716, 21.7 ])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0. , 0.294, 0.476, 0.476, 0.294, 0. ])
>>> distribution.sample(4).round(3)
array([ 0.32 , -1.082, 1.622, -0.036])
>>> distribution.mom(2).round(3)
1.0
"""
[docs] def __init__(self, scale=1, shift=0):
super(HyperbolicSecant, self).__init__(
dist=hyperbolic_secant(),
scale=scale,
shift=shift,
)