"""Fatigue-life distribution."""
import numpy
from scipy import special
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class fatigue_life(SimpleDistribution):
"""Fatigue-life distribution."""
def __init__(self, c=0):
super(fatigue_life, self).__init__(dict(c=c))
def _pdf(self, x, c):
output = (x + 1) / (2 * c * numpy.sqrt(2 * numpy.pi * x**3))
output *= numpy.exp(-((x - 1) ** 2) / (2.0 * x * c**2))
output[(x == 0) & numpy.isnan(output)] = 0
return output
def _cdf(self, x, c):
out = special.ndtr(1.0 / c * (numpy.sqrt(x) - 1.0 / numpy.sqrt(x)))
out = numpy.where(x == 0, 0, out)
return out
def _ppf(self, q, c):
tmp = c * special.ndtri(q)
out = numpy.where(
numpy.isfinite(tmp), 0.25 * (tmp + numpy.sqrt(tmp**2 + 4)) ** 2, tmp
)
return out
def _lower(self, c):
return (-4 * c + numpy.sqrt(16 * c**2 + 1)) ** 2
def _upper(self, c):
return (4 * c + numpy.sqrt(16 * c**2 + 1)) ** 2
[docs]class FatigueLife(ShiftScaleDistribution):
"""
Fatigue-Life or Birmbaum-Sanders distribution
Args:
shape (float, Distribution):
Shape parameter
scale (float, Distribution):
Scaling parameter
shift (float, Distribution):
Location parameter
Examples:
>>> distribution = chaospy.FatigueLife(0.5)
>>> distribution
FatigueLife(0.5)
>>> 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([ 0.056, 0.659, 0.881, 1.135, 1.519, 17.944])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0. , 0.869, 0.879, 0.682, 0.377, 0. ])
>>> distribution.sample(4).round(3)
array([1.218, 0.553, 2.23 , 0.978])
"""
[docs] def __init__(self, shape=1, scale=1, shift=0):
super(FatigueLife, self).__init__(
dist=fatigue_life(shape),
scale=scale,
shift=shift,
repr_args=[shape],
)