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Per A Brodtkorb 8 years ago
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wafo/stats/estimation.py
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@ -1,11 +1,11 @@
''' """
Contains FitDistribution and Profile class, which are Contains FitDistribution and Profile class, which are
important classes for fitting to various Continous and Discrete Probability important classes for fitting to various Continous and Discrete Probability
Distributions Distributions
Author: Per A. Brodtkorb 2008 Author: Per A. Brodtkorb 2008
''' """
from __future__ import division, absolute_import from __future__ import division, absolute_import
import warnings import warnings
@ -14,7 +14,7 @@ from scipy.stats._distn_infrastructure import check_random_state
from wafo.plotbackend import plotbackend as plt from wafo.plotbackend import plotbackend as plt
from wafo.misc import ecross, findcross from wafo.misc import ecross, findcross
from wafo.stats._constants import _EPS from wafo.stats._constants import _EPS
from scipy._lib.six import string_types # from scipy._lib.six import string_types
import numdifftools as nd # @UnresolvedImport import numdifftools as nd # @UnresolvedImport
from scipy import special from scipy import special
from scipy.linalg import pinv2 from scipy.linalg import pinv2
@ -204,7 +204,7 @@ def norm_ppf(q):
class Profile(object): class Profile(object):
''' """
Profile Log- likelihood or Product Spacing-function for phat[i]. Profile Log- likelihood or Product Spacing-function for phat[i].
Parameters Parameters
@ -260,7 +260,7 @@ class Profile(object):
>>> profile_phat_i.plot() >>> profile_phat_i.plot()
>>> phat_ci = profile_phat_i.get_bounds(alpha=0.1) >>> phat_ci = profile_phat_i.get_bounds(alpha=0.1)
''' """
def __init__(self, fit_dist, i=None, pmin=None, pmax=None, n=100, def __init__(self, fit_dist, i=None, pmin=None, pmax=None, n=100,
alpha=0.05): alpha=0.05):
@ -413,8 +413,8 @@ class Profile(object):
cl = self.alpha_cross_level - self.alpha_Lrange / 2.0 cl = self.alpha_cross_level - self.alpha_Lrange / 2.0
try: try:
t0 = ecross(self.args, self.data, ind1, cl) t0 = ecross(self.args, self.data, ind1, cl)
self.data.put(ind, cl) np.put(self.data, ind, cl)
self.args.put(ind, t0) np.put(self.args, ind, t0)
except IndexError as err: except IndexError as err:
warnings.warn(str(err)) warnings.warn(str(err))
@ -460,8 +460,8 @@ class Profile(object):
return pvec return pvec
def _get_pvec(self, phatfree0, p_opt): def _get_pvec(self, phatfree0, p_opt):
''' return proper interval for the variable to profile """ return proper interval for the variable to profile
''' """
if self.pmin is None or self.pmax is None: if self.pmin is None or self.pmax is None:
pmin, pmax = self._p_min_max(phatfree0, p_opt) pmin, pmax = self._p_min_max(phatfree0, p_opt)
return self._adaptive_pvec(p_opt, pmin, pmax) return self._adaptive_pvec(p_opt, pmin, pmax)
@ -506,12 +506,12 @@ class Profile(object):
return p_minmax_opt return p_minmax_opt
def _profile_fun(self, free_par, fix_par): def _profile_fun(self, free_par, fix_par):
''' Return negative of loglike or logps function """ Return negative of loglike or logps function
free_par - vector of free parameters free_par - vector of free parameters
fix_par - fixed parameter, i.e., either quantile (return level), fix_par - fixed parameter, i.e., either quantile (return level),
probability (return period) or distribution parameter probability (return period) or distribution parameter
''' """
par = self._par.copy() par = self._par.copy()
par[self.i_free] = free_par par[self.i_free] = free_par
@ -538,8 +538,8 @@ class Profile(object):
return bounds return bounds
def get_bounds(self, alpha=0.05): def get_bounds(self, alpha=0.05):
'''Return confidence interval for profiled parameter """Return confidence interval for profiled parameter
''' """
_assert_warn(self.alpha <= alpha, 'Might not be able to return bounds ' _assert_warn(self.alpha <= alpha, 'Might not be able to return bounds '
'with alpha less than {}'.format(self.alpha)) 'with alpha less than {}'.format(self.alpha))
@ -553,9 +553,9 @@ class Profile(object):
return bounds return bounds
def plot(self, axis=None): def plot(self, axis=None):
''' """
Plot profile function for p_opt with 100(1-alpha)% confidence interval. Plot profile function for p_opt with 100(1-alpha)% confidence interval.
''' """
if axis is None: if axis is None:
axis = plt.gca() axis = plt.gca()
@ -615,7 +615,7 @@ def plot_all_profiles(phats, plot=None):
class ProfileQuantile(Profile): class ProfileQuantile(Profile):
''' """
Profile Log- likelihood or Product Spacing-function for quantile. Profile Log- likelihood or Product Spacing-function for quantile.
Parameters Parameters
@ -680,7 +680,7 @@ class ProfileQuantile(Profile):
>>> profile_x = ProfileQuantile(phat, x) >>> profile_x = ProfileQuantile(phat, x)
>>> profile_x.plot() >>> profile_x.plot()
>>> x_ci = profile_x.get_bounds(alpha=0.2) >>> x_ci = profile_x.get_bounds(alpha=0.2)
''' """
def __init__(self, fit_dist, x, i=None, pmin=None, pmax=None, n=100, def __init__(self, fit_dist, x, i=None, pmin=None, pmax=None, n=100,
alpha=0.05, link=None): alpha=0.05, link=None):
self.x = x self.x = x
@ -713,7 +713,7 @@ class ProfileQuantile(Profile):
class ProfileProbability(Profile): class ProfileProbability(Profile):
''' Profile Log- likelihood or Product Spacing-function probability. """ Profile Log- likelihood or Product Spacing-function probability.
Parameters Parameters
---------- ----------
@ -776,7 +776,7 @@ class ProfileProbability(Profile):
>>> profile_logsf = ProfileProbability(phat, np.log(sf)) >>> profile_logsf = ProfileProbability(phat, np.log(sf))
>>> profile_logsf.plot() >>> profile_logsf.plot()
>>> logsf_ci = profile_logsf.get_bounds(alpha=0.2) >>> logsf_ci = profile_logsf.get_bounds(alpha=0.2)
''' """
def __init__(self, fit_dist, logsf, i=None, pmin=None, pmax=None, n=100, def __init__(self, fit_dist, logsf, i=None, pmin=None, pmax=None, n=100,
alpha=0.05, link=None): alpha=0.05, link=None):
self.x = fit_dist.isf(np.exp(logsf)) self.x = fit_dist.isf(np.exp(logsf))
@ -812,7 +812,7 @@ class ProfileProbability(Profile):
# Frozen RV class # Frozen RV class
class rv_frozen(object): class rv_frozen(object):
''' Frozen continous or discrete 1D Random Variable object (RV) """ Frozen continous or discrete 1D Random Variable object (RV)
Methods Methods
------- -------
@ -839,7 +839,7 @@ class rv_frozen(object):
expect(func, lb, ub, conditional=False) expect(func, lb, ub, conditional=False)
Calculate expected value of a function with respect to the Calculate expected value of a function with respect to the
distribution. distribution.
''' """
def __init__(self, dist, *args, **kwds): def __init__(self, dist, *args, **kwds):
# create a new instance # create a new instance
self.dist = dist # .__class__(**dist._ctor_param) self.dist = dist # .__class__(**dist._ctor_param)
@ -867,25 +867,25 @@ class rv_frozen(object):
self.dist._random_state = check_random_state(seed) self.dist._random_state = check_random_state(seed)
def pdf(self, x): def pdf(self, x):
''' Probability density function at x of the given RV.''' """ Probability density function at x of the given RV."""
return self.dist.pdf(x, *self.par) return self.dist.pdf(x, *self.par)
def logpdf(self, x): def logpdf(self, x):
return self.dist.logpdf(x, *self.par) return self.dist.logpdf(x, *self.par)
def cdf(self, x): def cdf(self, x):
'''Cumulative distribution function at x of the given RV.''' """Cumulative distribution function at x of the given RV."""
return self.dist.cdf(x, *self.par) return self.dist.cdf(x, *self.par)
def logcdf(self, x): def logcdf(self, x):
return self.dist.logcdf(x, *self.par) return self.dist.logcdf(x, *self.par)
def ppf(self, q): def ppf(self, q):
'''Percent point function (inverse of cdf) at q of the given RV.''' """Percent point function (inverse of cdf) at q of the given RV."""
return self.dist.ppf(q, *self.par) return self.dist.ppf(q, *self.par)
def isf(self, q): def isf(self, q):
'''Inverse survival function at q of the given RV.''' """Inverse survival function at q of the given RV."""
return self.dist.isf(q, *self.par) return self.dist.isf(q, *self.par)
def rvs(self, size=None, random_state=None): def rvs(self, size=None, random_state=None):
@ -893,14 +893,14 @@ class rv_frozen(object):
return self.dist.rvs(*self.par, **kwds) return self.dist.rvs(*self.par, **kwds)
def sf(self, x): def sf(self, x):
'''Survival function (1-cdf) at x of the given RV.''' """Survival function (1-cdf) at x of the given RV."""
return self.dist.sf(x, *self.par) return self.dist.sf(x, *self.par)
def logsf(self, x): def logsf(self, x):
return self.dist.logsf(x, *self.par) return self.dist.logsf(x, *self.par)
def stats(self, moments='mv'): def stats(self, moments='mv'):
''' Some statistics of the given RV''' """ Some statistics of the given RV"""
kwds = dict(moments=moments) kwds = dict(moments=moments)
return self.dist.stats(*self.par, **kwds) return self.dist.stats(*self.par, **kwds)
@ -923,7 +923,7 @@ class rv_frozen(object):
return self.dist.entropy(*self.par) return self.dist.entropy(*self.par)
def pmf(self, k): def pmf(self, k):
'''Probability mass function at k of the given RV''' """Probability mass function at k of the given RV"""
return self.dist.pmf(k, *self.par) return self.dist.pmf(k, *self.par)
def logpmf(self, k): def logpmf(self, k):
@ -945,7 +945,7 @@ class rv_frozen(object):
class FitDistribution(rv_frozen): class FitDistribution(rv_frozen):
''' """
Return estimators to shape, location, and scale from data Return estimators to shape, location, and scale from data
Starting points for the fit are given by input arguments. For any Starting points for the fit are given by input arguments. For any
@ -1037,10 +1037,10 @@ class FitDistribution(rv_frozen):
>>> profile_logsf = phat.profile_probability(log(sf)) >>> profile_logsf = phat.profile_probability(log(sf))
>>> profile_logsf.plot() >>> profile_logsf.plot()
>>> sf_ci = profile_logsf.get_bounds(alpha=0.2) >>> sf_ci = profile_logsf.get_bounds(alpha=0.2)
''' """
def __init__(self, dist, data, args=(), **kwds): def __init__(self, dist, data, args=(), **kwds):
extradoc = ''' extradoc = """
plotfitsummary() plotfitsummary()
Plot various diagnostic plots to asses quality of fit. Plot various diagnostic plots to asses quality of fit.
plotecdf() plotecdf()
@ -1069,7 +1069,7 @@ class FitDistribution(rv_frozen):
composed of letters ['mvsk'] specifying which moments to compute where composed of letters ['mvsk'] specifying which moments to compute where
'm' = mean, 'v' = variance, 's' = (Fisher's) skew and 'm' = mean, 'v' = variance, 's' = (Fisher's) skew and
'k' = (Fisher's) kurtosis. (default='mv') 'k' = (Fisher's) kurtosis. (default='mv')
''' """
# Member variables # Member variables
# ---------------- # ----------------
# data - data used in fitting # data - data used in fitting
@ -1087,7 +1087,7 @@ class FitDistribution(rv_frozen):
# par_lower - lower (1-alpha)% confidence bound for the parameters # par_lower - lower (1-alpha)% confidence bound for the parameters
# par_upper - upper (1-alpha)% confidence bound for the parameters # par_upper - upper (1-alpha)% confidence bound for the parameters
# #
# ''' # """
self.__doc__ = str(rv_frozen.__doc__) + extradoc self.__doc__ = str(rv_frozen.__doc__) + extradoc
self.dist = dist self.dist = dist
self.par_fix = None self.par_fix = None
@ -1153,9 +1153,9 @@ class FitDistribution(rv_frozen):
@staticmethod @staticmethod
def _hessian(nnlf, theta, data, eps=None): def _hessian(nnlf, theta, data, eps=None):
''' approximate hessian of nnlf where theta are the parameters """ approximate hessian of nnlf where theta are the parameters
(including loc and scale) (including loc and scale)
''' """
if eps is None: if eps is None:
eps = (_EPS) ** 0.25 eps = (_EPS) ** 0.25
num_par = len(theta) num_par = len(theta)
@ -1245,8 +1245,8 @@ class FitDistribution(rv_frozen):
return par_cov return par_cov
def _compute_cov(self): def _compute_cov(self):
'''Compute covariance """Compute covariance
''' """
H = np.asmatrix(self._hessian(self._fitfun, self.par, self.data)) H = np.asmatrix(self._hessian(self._fitfun, self.par, self.data))
# H = -nd.Hessian(lambda par: self._fitfun(par, self.data), # H = -nd.Hessian(lambda par: self._fitfun(par, self.data),
@ -1263,7 +1263,7 @@ class FitDistribution(rv_frozen):
return self._fitfun(phat, self.data) return self._fitfun(phat, self.data)
def profile(self, **kwds): def profile(self, **kwds):
''' """
Profile Log- likelihood or Log Product Spacing- function for phat[i] Profile Log- likelihood or Log Product Spacing- function for phat[i]
Examples Examples
@ -1281,11 +1281,11 @@ class FitDistribution(rv_frozen):
See also See also
-------- --------
Profile Profile
''' """
return Profile(self, **kwds) return Profile(self, **kwds)
def profile_quantile(self, x, **kwds): def profile_quantile(self, x, **kwds):
''' """
Profile Log- likelihood or Product Spacing-function for quantile. Profile Log- likelihood or Product Spacing-function for quantile.
Examples Examples
@ -1302,11 +1302,11 @@ class FitDistribution(rv_frozen):
>>> profile_x = phat.profile_quantile(x) >>> profile_x = phat.profile_quantile(x)
>>> profile_x.plot() >>> profile_x.plot()
>>> x_ci = profile_x.get_bounds(alpha=0.2) >>> x_ci = profile_x.get_bounds(alpha=0.2)
''' """
return ProfileQuantile(self, x, **kwds) return ProfileQuantile(self, x, **kwds)
def profile_probability(self, log_sf, **kwds): def profile_probability(self, log_sf, **kwds):
''' """
Profile Log- likelihood or Product Spacing-function for probability. Profile Log- likelihood or Product Spacing-function for probability.
Examples Examples
@ -1322,7 +1322,7 @@ class FitDistribution(rv_frozen):
>>> profile_logsf = phat.profile_probability(log_sf) >>> profile_logsf = phat.profile_probability(log_sf)
>>> profile_logsf.plot() >>> profile_logsf.plot()
>>> log_sf_ci = profile_logsf.get_bounds(alpha=0.2) >>> log_sf_ci = profile_logsf.get_bounds(alpha=0.2)
''' """
return ProfileProbability(self, log_sf, **kwds) return ProfileProbability(self, log_sf, **kwds)
def ci_sf(self, sf, alpha=0.05, i=2): def ci_sf(self, sf, alpha=0.05, i=2):
@ -1369,7 +1369,7 @@ class FitDistribution(rv_frozen):
return txt return txt
def plotfitsummary(self, axes=None, fig=None): def plotfitsummary(self, axes=None, fig=None):
''' Plot various diagnostic plots to asses the quality of the fit. """ Plot various diagnostic plots to asses the quality of the fit.
PLOTFITSUMMARY displays probability plot, density plot, residual PLOTFITSUMMARY displays probability plot, density plot, residual
quantile plot and residual probability plot. quantile plot and residual probability plot.
@ -1378,7 +1378,7 @@ class FitDistribution(rv_frozen):
PDF should follow the model and the residual plots will be linear. PDF should follow the model and the residual plots will be linear.
Other distribution types will introduce curvature in the residual Other distribution types will introduce curvature in the residual
plots. plots.
''' """
if axes is None: if axes is None:
fig, axes = plt.subplots(2, 2, figsize=(11, 8)) fig, axes = plt.subplots(2, 2, figsize=(11, 8))
fig.subplots_adjust(hspace=0.4, wspace=0.4) fig.subplots_adjust(hspace=0.4, wspace=0.4)
@ -1398,13 +1398,13 @@ class FitDistribution(rv_frozen):
pass pass
def plotesf(self, symb1='r-', symb2='b.', axis=None, plot_ci=False): def plotesf(self, symb1='r-', symb2='b.', axis=None, plot_ci=False):
''' Plot Empirical and fitted Survival Function """ Plot Empirical and fitted Survival Function
The purpose of the plot is to graphically assess whether The purpose of the plot is to graphically assess whether
the data could come from the fitted distribution. the data could come from the fitted distribution.
If so the empirical CDF should resemble the model CDF. If so the empirical CDF should resemble the model CDF.
Other distribution types will introduce deviations in the plot. Other distribution types will introduce deviations in the plot.
''' """
if axis is None: if axis is None:
axis = plt.gca() axis = plt.gca()
n = len(self.data) n = len(self.data)
@ -1422,13 +1422,13 @@ class FitDistribution(rv_frozen):
axis.set_title('Empirical SF plot') axis.set_title('Empirical SF plot')
def plotecdf(self, symb1='r-', symb2='b.', axis=None): def plotecdf(self, symb1='r-', symb2='b.', axis=None):
''' Plot Empirical and fitted Cumulative Distribution Function """ Plot Empirical and fitted Cumulative Distribution Function
The purpose of the plot is to graphically assess whether The purpose of the plot is to graphically assess whether
the data could come from the fitted distribution. the data could come from the fitted distribution.
If so the empirical CDF should resemble the model CDF. If so the empirical CDF should resemble the model CDF.
Other distribution types will introduce deviations in the plot. Other distribution types will introduce deviations in the plot.
''' """
if axis is None: if axis is None:
axis = plt.gca() axis = plt.gca()
n = len(self.data) n = len(self.data)
@ -1473,13 +1473,13 @@ class FitDistribution(rv_frozen):
return self._staircase(x, pdf) return self._staircase(x, pdf)
def plotepdf(self, symb1='r-', symb2='b-', axis=None): def plotepdf(self, symb1='r-', symb2='b-', axis=None):
'''Plot Empirical and fitted Probability Density Function """Plot Empirical and fitted Probability Density Function
The purpose of the plot is to graphically assess whether The purpose of the plot is to graphically assess whether
the data could come from the fitted distribution. the data could come from the fitted distribution.
If so the histogram should resemble the model density. If so the histogram should resemble the model density.
Other distribution types will introduce deviations in the plot. Other distribution types will introduce deviations in the plot.
''' """
if axis is None: if axis is None:
axis = plt.gca() axis = plt.gca()
x, pdf = self._get_empirical_pdf() x, pdf = self._get_empirical_pdf()
@ -1495,13 +1495,13 @@ class FitDistribution(rv_frozen):
axis.set_title('Density plot') axis.set_title('Density plot')
def plotresq(self, symb1='r-', symb2='b.', axis=None): def plotresq(self, symb1='r-', symb2='b.', axis=None):
'''PLOTRESQ displays a residual quantile plot. """PLOTRESQ displays a residual quantile plot.
The purpose of the plot is to graphically assess whether The purpose of the plot is to graphically assess whether
the data could come from the fitted distribution. If so the the data could come from the fitted distribution. If so the
plot will be linear. Other distribution types will introduce plot will be linear. Other distribution types will introduce
curvature in the plot. curvature in the plot.
''' """
if axis is None: if axis is None:
axis = plt.gca() axis = plt.gca()
n = len(self.data) n = len(self.data)
@ -1516,13 +1516,13 @@ class FitDistribution(rv_frozen):
axis.axis('equal') axis.axis('equal')
def plotresprb(self, symb1='r-', symb2='b.', axis=None): def plotresprb(self, symb1='r-', symb2='b.', axis=None):
''' PLOTRESPRB displays a residual probability plot. """ PLOTRESPRB displays a residual probability plot.
The purpose of the plot is to graphically assess whether The purpose of the plot is to graphically assess whether
the data could come from the fitted distribution. If so the the data could come from the fitted distribution. If so the
plot will be linear. Other distribution types will introduce curvature plot will be linear. Other distribution types will introduce curvature
in the plot. in the plot.
''' """
if axis is None: if axis is None:
axis = plt.gca() axis = plt.gca()
n = len(self.data) n = len(self.data)
@ -1538,13 +1538,13 @@ class FitDistribution(rv_frozen):
axis.axis([0, 1, 0, 1]) axis.axis([0, 1, 0, 1])
def _pvalue(self, theta, x, unknown_numpar=None): def _pvalue(self, theta, x, unknown_numpar=None):
''' Return P-value for the fit using Moran's negative log Product """ Return P-value for the fit using Moran's negative log Product
Spacings statistic Spacings statistic
where theta are the parameters (including loc and scale) where theta are the parameters (including loc and scale)
Note: the data in x must be sorted Note: the data in x must be sorted
''' """
dx = np.diff(x, axis=0) dx = np.diff(x, axis=0)
tie = (dx == 0) tie = (dx == 0)
if np.any(tie): if np.any(tie):

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