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