"""(Non-central) F distribution."""
import numpy
from scipy import special
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class f(SimpleDistribution):
"""F distribution."""
def __init__(self, dfn, dfd, nc):
super(f, self).__init__(
parameters=dict(dfn=dfn, dfd=dfd, nc=nc),
repr_args=[dfn, dfd, "nc=%s" % nc],
)
def _pdf(self, x, dfn, dfd, nc):
n1, n2 = dfn, dfd
term = (
-nc / 2.0
+ nc * n1 * x / (2 * (n2 + n1 * x))
+ special.gammaln(n1 / 2.0)
+ special.gammaln(1 + n2 / 2.0)
)
term -= special.gammaln((n1 + n2) / 2.0)
Px = numpy.exp(term)
Px *= n1 ** (n1 / 2.0) * n2 ** (n2 / 2.0) * x ** (n1 / 2.0 - 1)
Px *= (n2 + n1 * x) ** (-(n1 + n2) / 2.0)
Px *= special.assoc_laguerre(
-nc * n1 * x / (2.0 * (n2 + n1 * x)), n2 / 2.0, n1 / 2.0 - 1
)
Px /= special.beta(n1 / 2.0, n2 / 2.0)
return Px
def _cdf(self, x, dfn, dfd, nc):
return special.ncfdtr(dfn, dfd, nc, x)
def _ppf(self, q, dfn, dfd, nc):
return numpy.where(
q == 1, self._upper(dfn, dfd, nc), special.ncfdtri(dfn, dfd, nc, q)
)
def _lower(self, dfn, dfd, nc):
return 0.0
def _upper(self, dfn, dfd, nc):
return special.ncfdtri(dfn, dfd, nc, 1 - 1e-10)
[docs]class F(ShiftScaleDistribution):
"""
(Non-central) F or Fisher-Snedecor distribution.
Args:
n (float, Distribution):
Degres of freedom for numerator
m (float, Distribution):
Degres of freedom for denominator
nc (float, Distribution):
Non-centrality parameter
scale (float, Distribution):
Scaling parameter
shift (float, Distribution):
Location parameter
Examples:
>>> distribution = chaospy.F(10, 10, 0)
>>> distribution
F(10, 10, nc=0)
>>> 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. , 0.578, 0.848, 1.179, 1.732, 261.403])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0. , 0.734, 0.701, 0.505, 0.245, 0. ])
>>> distribution.sample(4).round(3)
array([1.292, 0.455, 2.984, 0.971])
"""
[docs] def __init__(self, n=2, m=10, nc=0, shift=0, scale=1):
super(F, self).__init__(
dist=f(n, m, nc),
shift=shift,
scale=scale,
repr_args=[n, m, "nc=%s" % nc],
)