"""Pareto type 1 distribution."""
import numpy
from scipy import special
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class pareto1(SimpleDistribution):
"""Pareto type 1 distribution."""
def __init__(self, b):
super(pareto1, self).__init__(dict(b=b))
def _pdf(self, x, b):
return b * x ** (-b - 1)
def _cdf(self, x, b):
return 1 - x**-b
def _ppf(self, q, b):
return pow(1 - q, -1.0 / b)
def _lower(self, b):
return 1.0
def _upper(self, b):
return pow(1e12, 1.0 / b)
[docs]class Pareto1(ShiftScaleDistribution):
"""
Pareto type 1 distribution.
Lower threshold at scale+loc and survival: x^-shape
Args:
shape (float, Distribution):
Tail index parameter
scale (float, Distribution):
Scaling parameter
shift (float, Distribution):
Location parameter
Examples:
>>> distribution = chaospy.Pareto1(15)
>>> distribution
Pareto1(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([1. , 1.015, 1.035, 1.063, 1.113, 6.31 ])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([15. , 11.823, 8.699, 5.644, 2.695, 0. ])
>>> distribution.sample(4).round(3)
array([1.073, 1.008, 1.222, 1.045])
"""
[docs] def __init__(self, shape=1, scale=1, shift=0):
super(Pareto1, self).__init__(
dist=pareto1(shape),
scale=scale,
shift=shift,
repr_args=[shape],
)