485 lines
16 KiB
Python
485 lines
16 KiB
Python
## copied from nonlinear_transform_gen.py
|
|
|
|
''' A class for the distribution of a non-linear monotonic transformation of a continuous random variable
|
|
|
|
simplest usage:
|
|
example: create log-gamma distribution, i.e. y = log(x),
|
|
where x is gamma distributed (also available in scipy.stats)
|
|
loggammaexpg = Transf_gen(stats.gamma, np.log, np.exp)
|
|
|
|
example: what is the distribution of the discount factor y=1/(1+x)
|
|
where interest rate x is normally distributed with N(mux,stdx**2)')?
|
|
(just to come up with a story that implies a nice transformation)
|
|
invnormalg = Transf_gen(stats.norm, inversew, inversew_inv, decr=True, a=-np.inf)
|
|
|
|
This class does not work well for distributions with difficult shapes,
|
|
e.g. 1/x where x is standard normal, because of the singularity and jump at zero.
|
|
|
|
Note: I'm working from my version of scipy.stats.distribution.
|
|
But this script runs under scipy 0.6.0 (checked with numpy: 1.2.0rc2 and python 2.4)
|
|
|
|
This is not yet thoroughly tested, polished or optimized
|
|
|
|
TODO:
|
|
* numargs handling is not yet working properly, numargs needs to be specified (default = 0 or 1)
|
|
* feeding args and kwargs to underlying distribution is untested and incomplete
|
|
* distinguish args and kwargs for the transformed and the underlying distribution
|
|
- currently all args and no kwargs are transmitted to underlying distribution
|
|
- loc and scale only work for transformed, but not for underlying distribution
|
|
- possible to separate args for transformation and underlying distribution parameters
|
|
|
|
* add _rvs as method, will be faster in many cases
|
|
|
|
|
|
Created on Tuesday, October 28, 2008, 12:40:37 PM
|
|
Author: josef-pktd
|
|
License: BSD
|
|
|
|
'''
|
|
from scipy import stats
|
|
from scipy.stats import distributions
|
|
import numpy as np
|
|
|
|
|
|
def get_u_argskwargs(**kwargs):
|
|
# Todo: What's this? wrong spacing, used in Transf_gen TransfTwo_gen
|
|
u_kwargs = {k.replace('u_', '', 1): v for k, v in kwargs.items()
|
|
if k.startswith('u_')}
|
|
u_args = u_kwargs.pop('u_args', None)
|
|
return u_args, u_kwargs
|
|
|
|
|
|
class Transf_gen(distributions.rv_continuous):
|
|
'''a class for non-linear monotonic transformation of a continuous random variable
|
|
|
|
'''
|
|
|
|
def __init__(self, kls, func, funcinv, *args, **kwargs):
|
|
# print(args
|
|
# print(kwargs
|
|
|
|
self.func = func
|
|
self.funcinv = funcinv
|
|
# explicit for self.__dict__.update(kwargs)
|
|
# need to set numargs because inspection does not work
|
|
self.numargs = kwargs.pop('numargs', 0)
|
|
# print(self.numargs
|
|
name = kwargs.pop('name', 'transfdist')
|
|
longname = kwargs.pop('longname', 'Non-linear transformed distribution')
|
|
extradoc = kwargs.pop('extradoc', None)
|
|
a = kwargs.pop('a', -np.inf)
|
|
b = kwargs.pop('b', np.inf)
|
|
self.decr = kwargs.pop('decr', False)
|
|
# defines whether it is a decreasing (True)
|
|
# or increasing (False) monotonic transformation
|
|
|
|
self.u_args, self.u_kwargs = get_u_argskwargs(**kwargs)
|
|
self.kls = kls # (self.u_args, self.u_kwargs)
|
|
# possible to freeze the underlying distribution
|
|
|
|
super().__init__(
|
|
a=a, b=b, name=name, shapes=kls.shapes, longname=longname,
|
|
)
|
|
|
|
def _cdf(self, x, *args, **kwargs):
|
|
# print(args
|
|
if not self.decr:
|
|
return self.kls._cdf(self.funcinv(x), *args, **kwargs)
|
|
# note scipy _cdf only take *args not *kwargs
|
|
else:
|
|
return 1.0 - self.kls._cdf(self.funcinv(x), *args, **kwargs)
|
|
|
|
def _ppf(self, q, *args, **kwargs):
|
|
if not self.decr:
|
|
return self.func(self.kls._ppf(q, *args, **kwargs))
|
|
else:
|
|
return self.func(self.kls._ppf(1 - q, *args, **kwargs))
|
|
|
|
|
|
def inverse(x):
|
|
return np.divide(1.0, x)
|
|
|
|
|
|
mux, stdx = 0.05, 0.1
|
|
mux, stdx = 9.0, 1.0
|
|
|
|
|
|
def inversew(x):
|
|
return 1.0 / (1 + mux + x * stdx)
|
|
|
|
|
|
def inversew_inv(x):
|
|
return (1.0 / x - 1.0 - mux) / stdx # .np.divide(1.0,x)-10
|
|
|
|
|
|
def identit(x):
|
|
return x
|
|
|
|
|
|
invdnormalg = Transf_gen(stats.norm, inversew, inversew_inv, decr=True, # a=-np.inf,
|
|
numargs=0, name='discf', longname='normal-based discount factor',
|
|
# extradoc = '\ndistribution of discount factor y=1/(1+x)) with x N(0.05,0.1**2)'
|
|
)
|
|
|
|
lognormalg = Transf_gen(stats.norm, np.exp, np.log,
|
|
numargs=2, a=0, name='lnnorm',
|
|
longname='Exp transformed normal',
|
|
# extradoc = '\ndistribution of y = exp(x), with x standard normal'
|
|
# 'precision for moment andstats is not very high, 2-3 decimals'
|
|
)
|
|
|
|
loggammaexpg = Transf_gen(stats.gamma, np.log, np.exp, numargs=1)
|
|
|
|
## copied form nonlinear_transform_short.py
|
|
|
|
'''univariate distribution of a non-linear monotonic transformation of a
|
|
random variable
|
|
|
|
'''
|
|
|
|
|
|
class ExpTransf_gen(distributions.rv_continuous):
|
|
'''Distribution based on log/exp transformation
|
|
|
|
the constructor can be called with a distribution class
|
|
and generates the distribution of the transformed random variable
|
|
|
|
'''
|
|
|
|
def __init__(self, kls, *args, **kwargs):
|
|
# print(args
|
|
# print(kwargs
|
|
# explicit for self.__dict__.update(kwargs)
|
|
if 'numargs' in kwargs:
|
|
self.numargs = kwargs['numargs']
|
|
else:
|
|
self.numargs = 1
|
|
if 'name' in kwargs:
|
|
name = kwargs['name']
|
|
else:
|
|
name = 'Log transformed distribution'
|
|
if 'a' in kwargs:
|
|
a = kwargs['a']
|
|
else:
|
|
a = 0
|
|
super().__init__(a=a, name=name)
|
|
self.kls = kls
|
|
|
|
def _cdf(self, x, *args):
|
|
# print(args
|
|
return self.kls._cdf(np.log(x), *args)
|
|
|
|
def _ppf(self, q, *args):
|
|
return np.exp(self.kls._ppf(q, *args))
|
|
|
|
|
|
class LogTransf_gen(distributions.rv_continuous):
|
|
'''Distribution based on log/exp transformation
|
|
|
|
the constructor can be called with a distribution class
|
|
and generates the distribution of the transformed random variable
|
|
|
|
'''
|
|
|
|
def __init__(self, kls, *args, **kwargs):
|
|
# explicit for self.__dict__.update(kwargs)
|
|
if 'numargs' in kwargs:
|
|
self.numargs = kwargs['numargs']
|
|
else:
|
|
self.numargs = 1
|
|
if 'name' in kwargs:
|
|
name = kwargs['name']
|
|
else:
|
|
name = 'Log transformed distribution'
|
|
if 'a' in kwargs:
|
|
a = kwargs['a']
|
|
else:
|
|
a = 0
|
|
|
|
super().__init__(a=a, name=name)
|
|
self.kls = kls
|
|
|
|
def _cdf(self, x, *args):
|
|
# print(args
|
|
return self.kls._cdf(np.exp(x), *args)
|
|
|
|
def _ppf(self, q, *args):
|
|
return np.log(self.kls._ppf(q, *args))
|
|
|
|
|
|
def examples_transf():
|
|
##lognormal = ExpTransf(a=0.0, xa=-10.0, name = 'Log transformed normal')
|
|
##print(lognormal.cdf(1)
|
|
##print(stats.lognorm.cdf(1,1)
|
|
##print(lognormal.stats()
|
|
##print(stats.lognorm.stats(1)
|
|
##print(lognormal.rvs(size=10)
|
|
|
|
print('Results for lognormal')
|
|
lognormalg = ExpTransf_gen(stats.norm, a=0, name='Log transformed normal general')
|
|
print(lognormalg.cdf(1))
|
|
print(stats.lognorm.cdf(1, 1))
|
|
print(lognormalg.stats())
|
|
print(stats.lognorm.stats(1))
|
|
print(lognormalg.rvs(size=5))
|
|
|
|
##print('Results for loggamma'
|
|
##loggammag = ExpTransf_gen(stats.gamma)
|
|
##print(loggammag._cdf(1,10)
|
|
##print(stats.loggamma.cdf(1,10)
|
|
|
|
print('Results for expgamma')
|
|
loggammaexpg = LogTransf_gen(stats.gamma)
|
|
print(loggammaexpg._cdf(1, 10))
|
|
print(stats.loggamma.cdf(1, 10))
|
|
print(loggammaexpg._cdf(2, 15))
|
|
print(stats.loggamma.cdf(2, 15))
|
|
|
|
# this requires change in scipy.stats.distribution
|
|
# print(loggammaexpg.cdf(1,10)
|
|
|
|
print('Results for loglaplace')
|
|
loglaplaceg = LogTransf_gen(stats.laplace)
|
|
print(loglaplaceg._cdf(2, 10))
|
|
print(stats.loglaplace.cdf(2, 10))
|
|
loglaplaceexpg = ExpTransf_gen(stats.laplace)
|
|
print(loglaplaceexpg._cdf(2, 10))
|
|
|
|
|
|
## copied from transformtwo.py
|
|
|
|
'''
|
|
Created on Apr 28, 2009
|
|
|
|
@author: Josef Perktold
|
|
'''
|
|
|
|
''' A class for the distribution of a non-linear u-shaped or hump shaped transformation of a
|
|
continuous random variable
|
|
|
|
This is a companion to the distributions of non-linear monotonic transformation to the case
|
|
when the inverse mapping is a 2-valued correspondence, for example for absolute value or square
|
|
|
|
simplest usage:
|
|
example: create squared distribution, i.e. y = x**2,
|
|
where x is normal or t distributed
|
|
|
|
|
|
This class does not work well for distributions with difficult shapes,
|
|
e.g. 1/x where x is standard normal, because of the singularity and jump at zero.
|
|
|
|
|
|
This verifies for normal - chi2, normal - halfnorm, foldnorm, and t - F
|
|
|
|
TODO:
|
|
* numargs handling is not yet working properly,
|
|
numargs needs to be specified (default = 0 or 1)
|
|
* feeding args and kwargs to underlying distribution works in t distribution example
|
|
* distinguish args and kwargs for the transformed and the underlying distribution
|
|
- currently all args and no kwargs are transmitted to underlying distribution
|
|
- loc and scale only work for transformed, but not for underlying distribution
|
|
- possible to separate args for transformation and underlying distribution parameters
|
|
|
|
* add _rvs as method, will be faster in many cases
|
|
|
|
'''
|
|
|
|
|
|
class TransfTwo_gen(distributions.rv_continuous):
|
|
'''Distribution based on a non-monotonic (u- or hump-shaped transformation)
|
|
|
|
the constructor can be called with a distribution class, and functions
|
|
that define the non-linear transformation.
|
|
and generates the distribution of the transformed random variable
|
|
|
|
Note: the transformation, it's inverse and derivatives need to be fully
|
|
specified: func, funcinvplus, funcinvminus, derivplus, derivminus.
|
|
Currently no numerical derivatives or inverse are calculated
|
|
|
|
This can be used to generate distribution instances similar to the
|
|
distributions in scipy.stats.
|
|
|
|
'''
|
|
|
|
# a class for non-linear non-monotonic transformation of a continuous random variable
|
|
def __init__(self, kls, func, funcinvplus, funcinvminus, derivplus,
|
|
derivminus, *args, **kwargs):
|
|
# print(args
|
|
# print(kwargs
|
|
|
|
self.func = func
|
|
self.funcinvplus = funcinvplus
|
|
self.funcinvminus = funcinvminus
|
|
self.derivplus = derivplus
|
|
self.derivminus = derivminus
|
|
# explicit for self.__dict__.update(kwargs)
|
|
# need to set numargs because inspection does not work
|
|
self.numargs = kwargs.pop('numargs', 0)
|
|
# print(self.numargs
|
|
name = kwargs.pop('name', 'transfdist')
|
|
longname = kwargs.pop('longname', 'Non-linear transformed distribution')
|
|
extradoc = kwargs.pop('extradoc', None)
|
|
a = kwargs.pop('a', -np.inf) # attached to self in super
|
|
b = kwargs.pop('b', np.inf) # self.a, self.b would be overwritten
|
|
self.shape = kwargs.pop('shape', False)
|
|
# defines whether it is a `u` shaped or `hump' shaped
|
|
# transformation
|
|
|
|
self.u_args, self.u_kwargs = get_u_argskwargs(**kwargs)
|
|
self.kls = kls # (self.u_args, self.u_kwargs)
|
|
# possible to freeze the underlying distribution
|
|
|
|
super().__init__(
|
|
a=a, b=b, name=name, shapes=kls.shapes, longname=longname
|
|
)
|
|
|
|
def _rvs(self, *args):
|
|
self.kls._size = self._size # size attached to self, not function argument
|
|
return self.func(self.kls._rvs(*args))
|
|
|
|
def _pdf(self, x, *args, **kwargs):
|
|
# print(args
|
|
if self.shape == 'u':
|
|
signpdf = 1
|
|
elif self.shape == 'hump':
|
|
signpdf = -1
|
|
else:
|
|
raise ValueError('shape can only be `u` or `hump`')
|
|
|
|
return signpdf * (self.derivplus(x) * self.kls._pdf(self.funcinvplus(x), *args, **kwargs) -
|
|
self.derivminus(x) * self.kls._pdf(self.funcinvminus(x), *args,
|
|
**kwargs))
|
|
# note scipy _cdf only take *args not *kwargs
|
|
|
|
def _cdf(self, x, *args, **kwargs):
|
|
# print(args
|
|
if self.shape == 'u':
|
|
return self.kls._cdf(self.funcinvplus(x), *args, **kwargs) - \
|
|
self.kls._cdf(self.funcinvminus(x), *args, **kwargs)
|
|
# note scipy _cdf only take *args not *kwargs
|
|
else:
|
|
return 1.0 - self._sf(x, *args, **kwargs)
|
|
|
|
def _sf(self, x, *args, **kwargs):
|
|
# print(args
|
|
if self.shape == 'hump':
|
|
return self.kls._cdf(self.funcinvplus(x), *args, **kwargs) - \
|
|
self.kls._cdf(self.funcinvminus(x), *args, **kwargs)
|
|
# note scipy _cdf only take *args not *kwargs
|
|
else:
|
|
return 1.0 - self._cdf(x, *args, **kwargs)
|
|
|
|
def _munp(self, n, *args, **kwargs):
|
|
return self._mom0_sc(n, *args)
|
|
|
|
|
|
# ppf might not be possible in general case?
|
|
# should be possible in symmetric case
|
|
# def _ppf(self, q, *args, **kwargs):
|
|
# if self.shape == 'u':
|
|
# return self.func(self.kls._ppf(q,*args, **kwargs))
|
|
# elif self.shape == 'hump':
|
|
# return self.func(self.kls._ppf(1-q,*args, **kwargs))
|
|
|
|
# TODO: rename these functions to have unique names
|
|
|
|
class SquareFunc:
|
|
'''class to hold quadratic function with inverse function and derivative
|
|
|
|
using instance methods instead of class methods, if we want extension
|
|
to parametrized function
|
|
'''
|
|
|
|
def inverseplus(self, x):
|
|
return np.sqrt(x)
|
|
|
|
def inverseminus(self, x):
|
|
return 0.0 - np.sqrt(x)
|
|
|
|
def derivplus(self, x):
|
|
return 0.5 / np.sqrt(x)
|
|
|
|
def derivminus(self, x):
|
|
return 0.0 - 0.5 / np.sqrt(x)
|
|
|
|
def squarefunc(self, x):
|
|
return np.power(x, 2)
|
|
|
|
|
|
sqfunc = SquareFunc()
|
|
|
|
squarenormalg = TransfTwo_gen(stats.norm, sqfunc.squarefunc, sqfunc.inverseplus,
|
|
sqfunc.inverseminus, sqfunc.derivplus, sqfunc.derivminus,
|
|
shape='u', a=0.0, b=np.inf,
|
|
numargs=0, name='squarenorm', longname='squared normal distribution',
|
|
# extradoc = '\ndistribution of the square of a normal random variable' +\
|
|
# ' y=x**2 with x N(0.0,1)'
|
|
)
|
|
# u_loc=l, u_scale=s)
|
|
squaretg = TransfTwo_gen(stats.t, sqfunc.squarefunc, sqfunc.inverseplus,
|
|
sqfunc.inverseminus, sqfunc.derivplus, sqfunc.derivminus,
|
|
shape='u', a=0.0, b=np.inf,
|
|
numargs=1, name='squarenorm', longname='squared t distribution',
|
|
# extradoc = '\ndistribution of the square of a t random variable' +\
|
|
# ' y=x**2 with x t(dof,0.0,1)'
|
|
)
|
|
|
|
|
|
def inverseplus(x):
|
|
return np.sqrt(-x)
|
|
|
|
|
|
def inverseminus(x):
|
|
return 0.0 - np.sqrt(-x)
|
|
|
|
|
|
def derivplus(x):
|
|
return 0.0 - 0.5 / np.sqrt(-x)
|
|
|
|
|
|
def derivminus(x):
|
|
return 0.5 / np.sqrt(-x)
|
|
|
|
|
|
def negsquarefunc(x):
|
|
return -np.power(x, 2)
|
|
|
|
|
|
negsquarenormalg = TransfTwo_gen(stats.norm, negsquarefunc, inverseplus, inverseminus,
|
|
derivplus, derivminus, shape='hump', a=-np.inf, b=0.0,
|
|
numargs=0, name='negsquarenorm',
|
|
longname='negative squared normal distribution',
|
|
# extradoc = '\ndistribution of the negative square of a normal random variable' +\
|
|
# ' y=-x**2 with x N(0.0,1)'
|
|
)
|
|
|
|
|
|
# u_loc=l, u_scale=s)
|
|
|
|
def inverseplus(x):
|
|
return x
|
|
|
|
|
|
def inverseminus(x):
|
|
return 0.0 - x
|
|
|
|
|
|
def derivplus(x):
|
|
return 1.0
|
|
|
|
|
|
def derivminus(x):
|
|
return 0.0 - 1.0
|
|
|
|
|
|
def absfunc(x):
|
|
return np.abs(x)
|
|
|
|
|
|
absnormalg = TransfTwo_gen(stats.norm, np.abs, inverseplus, inverseminus,
|
|
derivplus, derivminus, shape='u', a=0.0, b=np.inf,
|
|
numargs=0, name='absnorm', longname='absolute of normal distribution',
|
|
# extradoc = '\ndistribution of the absolute value of a normal random variable' +\
|
|
# ' y=abs(x) with x N(0,1)'
|
|
)
|