"""Mielke's beta-kappa distribution."""
import numpy
from scipy import special
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class mielke(SimpleDistribution):
"""Mielke's beta-kappa distribution."""
def __init__(self, k, s):
super(mielke, self).__init__(dict(k=k, s=s))
def _pdf(self, x, k, s):
return k * x ** (k - 1.0) / (1.0 + x**s) ** (1.0 + k * 1.0 / s)
def _cdf(self, x, k, s):
return x**k / (1.0 + x**s) ** (k * 1.0 / s)
def _ppf(self, q, k, s):
qsk = pow(q, s * 1.0 / k)
return pow(qsk / (1.0 - qsk), 1.0 / s)
def _lower(self, k, s):
return 0.0
def _upper(self, k, s):
qsk = pow(1 - 1e-10, s * 1.0 / k)
return pow(qsk / (1.0 - qsk), 1.0 / s)
[docs]class Mielke(ShiftScaleDistribution):
"""
Mielke's beta-kappa distribution
Args:
kappa (float, Distribution):
First shape parameter
expo (float, Distribution):
Second shape parameter
scale (float, Distribution):
Scaling parameter
shift (float, Distribution):
Location parameter
Examples:
>>> distribution = chaospy.Mielke(kappa=1.5, expo=15)
>>> distribution
Mielke(1.5, 15)
>>> 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. , 0.342, 0.543, 0.712, 0.868, 3.981])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0. , 0.877, 1.105, 1.257, 1.234, 0. ])
>>> distribution.sample(4).round(3)
array([0.754, 0.236, 1.028, 0.615])
"""
[docs] def __init__(self, kappa=1, expo=1, scale=1, shift=0):
super(Mielke, self).__init__(
dist=mielke(kappa, expo),
scale=scale,
shift=shift,
repr_args=[kappa, expo],
)