# Source code for statsmodels.sandbox.distributions.transformed



## 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 statsmodels.compat.python import iteritems

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 = dict((k.replace('u_','',1),v) for k,v in iteritems(kwargs)
if k.startswith('u_'))
u_args = u_kwargs.pop('u_args',None)
return u_args, u_kwargs

[docs]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(Transf_gen,self).__init__(a=a, b=b, name = name,
shapes=kls.shapes,
longname = longname,
extradoc = extradoc)

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

'''

[docs]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(ExpTransf_gen,self).__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))

[docs]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(LogTransf_gen,self).__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

'''

[docs]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(TransfTwo_gen,self).__init__(a=a, b=b,
name = name,
shapes=kls.shapes,
longname = longname,
extradoc = extradoc)

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

[docs]class SquareFunc(object):
'''class to hold quadratic function with inverse function and derivative

using instance methods instead of class methods, if we want extension
to parametrized function
'''
[docs]    def inverseplus(self, x):
return np.sqrt(x)

[docs]    def inverseminus(self, x):
return 0.0 - np.sqrt(x)

[docs]    def derivplus(self, x):
return 0.5/np.sqrt(x)

[docs]    def derivminus(self, x):
return 0.0 - 0.5/np.sqrt(x)

[docs]    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)')
`