"""
Created on Wed Jul 28 08:28:04 2010

Author: josef-pktd
"""
import numpy as np

from scipy import stats, special, optimize
import statsmodels.api as sm
from statsmodels.base.model import GenericLikelihoodModel
from statsmodels.tools.numdiff import approx_hess

#import for kstest based estimation
#should be replace
# FIXME: importing these patches scipy distribution classes in-place.
#  Do not do this.
import statsmodels.sandbox.distributions.sppatch  # noqa:F401


#redefine some shortcuts
np_log = np.log
np_pi = np.pi
sps_gamln = special.gammaln


def maxabs(arr1, arr2):
    return np.max(np.abs(arr1 - arr2))

def maxabsrel(arr1, arr2):
    return np.max(np.abs(arr2 / arr1 - 1))

#global
store_params = []

class MyT(GenericLikelihoodModel):
    '''Maximum Likelihood Estimation of Linear Model with t-distributed errors

    This is an example for generic MLE which has the same
    statistical model as discretemod.Poisson.

    Except for defining the negative log-likelihood method, all
    methods and results are generic. Gradients and Hessian
    and all resulting statistics are based on numerical
    differentiation.

    '''


    def loglike(self, params):
        return -self.nloglikeobs(params).sum(0)

    # copied from discretemod.Poisson
    def nloglikeobs(self, params):
        """
        Loglikelihood of Poisson model

        Parameters
        ----------
        params : array_like
            The parameters of the model.

        Returns
        -------
        The log likelihood of the model evaluated at `params`

        Notes
        -----
        .. math:: \\ln L=\\sum_{i=1}^{n}\\left[-\\lambda_{i}+y_{i}x_{i}^{\\prime}\\beta-\\ln y_{i}!\\right]
        """
        #print len(params),
        store_params.append(params)
        if self.fixed_params is not None:
            #print 'using fixed'
            params = self.expandparams(params)

        beta = params[:-2]
        df = params[-2]
        scale = params[-1]
        loc = np.dot(self.exog, beta)
        endog = self.endog
        x = (endog - loc)/scale
        #next part is stats.t._logpdf
        lPx = sps_gamln((df+1)/2) - sps_gamln(df/2.)
        lPx -= 0.5*np_log(df*np_pi) + (df+1)/2.*np_log(1+(x**2)/df)
        lPx -= np_log(scale)  # correction for scale
        return -lPx


#Example:
np.random.seed(98765678)
nobs = 1000
nvars = 6
df = 5
rvs = np.random.randn(nobs, nvars-1)
data_exog = sm.add_constant(rvs, prepend=False)
xbeta = 0.9 + 0.1*rvs.sum(1)
data_endog = xbeta + 0.1*np.random.standard_t(df, size=nobs)
print(data_endog.var())

res_ols = sm.OLS(data_endog, data_exog).fit()
print(res_ols.scale)
print(np.sqrt(res_ols.scale))
print(res_ols.params)
kurt = stats.kurtosis(res_ols.resid)
df_fromkurt = 6./kurt + 4
print(stats.t.stats(df_fromkurt, moments='mvsk'))
print(stats.t.stats(df, moments='mvsk'))

modp = MyT(data_endog, data_exog)
start_value = 0.1*np.ones(data_exog.shape[1]+2)
#start_value = np.zeros(data_exog.shape[1]+2)
#start_value[:nvars] = sm.OLS(data_endog, data_exog).fit().params
start_value[:nvars] = res_ols.params
start_value[-2] = df_fromkurt #10
start_value[-1] = np.sqrt(res_ols.scale) #0.5
modp.start_params = start_value

#adding fixed parameters

fixdf = np.nan * np.zeros(modp.start_params.shape)
fixdf[-2] = 100

fixone = 0
if fixone:
    modp.fixed_params = fixdf
    modp.fixed_paramsmask = np.isnan(fixdf)
    modp.start_params = modp.start_params[modp.fixed_paramsmask]
else:
    modp.fixed_params = None
    modp.fixed_paramsmask = None


resp = modp.fit(start_params = modp.start_params, disp=1, method='nm')#'newton')
#resp = modp.fit(start_params = modp.start_params, disp=1, method='newton')
print('\nestimation results t-dist')
print(resp.params)
print(resp.bse)
resp2 = modp.fit(start_params = resp.params, method='Newton')
print('using Newton')
print(resp2.params)
print(resp2.bse)


hb=-approx_hess(modp.start_params, modp.loglike, epsilon=-1e-4)
tmp = modp.loglike(modp.start_params)
print(tmp.shape)
#np.linalg.eigh(np.linalg.inv(hb))[0]

pp=np.array(store_params)
print(pp.min(0))
print(pp.max(0))




##################### Example: Pareto
# estimating scale does not work yet, a bug somewhere ?
# fit_ks works well, but no bse or other result statistics yet


class MyPareto(GenericLikelihoodModel):
    '''Maximum Likelihood Estimation pareto distribution

    first version: iid case, with constant parameters
    '''

    #copied from stats.distribution
    def pdf(self, x, b):
        return b * x**(-b-1)

    def loglike(self, params):
        return -self.nloglikeobs(params).sum(0)

    def nloglikeobs(self, params):
        #print params.shape
        if self.fixed_params is not None:
            #print 'using fixed'
            params = self.expandparams(params)
        b = params[0]
        loc = params[1]
        scale = params[2]
        #loc = np.dot(self.exog, beta)
        endog = self.endog
        x = (endog - loc)/scale
        logpdf = np_log(b) - (b+1.)*np_log(x)  #use np_log(1 + x) for Pareto II
        logpdf -= np.log(scale)
        #lb = loc + scale
        #logpdf[endog<lb] = -inf
        #import pdb; pdb.set_trace()
        logpdf[x<1] = -10000 #-np.inf
        return -logpdf

    def fit_ks(self):
        '''fit Pareto with nested optimization

        originally published on stackoverflow
        this does not trim lower values during ks optimization

        '''
        rvs = self.endog
        rvsmin = rvs.min()
        fixdf = np.nan * np.ones(3)
        self.fixed_params = fixdf
        self.fixed_paramsmask = np.isnan(fixdf)

        def pareto_ks(loc, rvs):
            #start_scale = rvs.min() - loc # not used yet
            #est = self.fit_fr(rvs, 1., frozen=[np.nan, loc, np.nan])
            self.fixed_params[1] = loc
            est = self.fit(start_params=self.start_params[self.fixed_paramsmask]).params
            #est = self.fit(start_params=self.start_params, method='nm').params
            args = (est[0], loc, est[1])
            return stats.kstest(rvs,'pareto',args)[0]

        locest = optimize.fmin(pareto_ks, rvsmin - 1.5, (rvs,))
        est = stats.pareto.fit_fr(rvs, 0., frozen=[np.nan, locest, np.nan])
        args = (est[0], locest[0], est[1])
        return args


    def fit_ks1_trim(self):
        '''fit Pareto with nested optimization

        originally published on stackoverflow

        '''
        self.nobs = self.endog.shape[0]
        rvs = np.sort(self.endog)
        rvsmin = rvs.min()

        def pareto_ks(loc, rvs):
            #start_scale = rvs.min() - loc # not used yet
            est = stats.pareto.fit_fr(rvs, frozen=[np.nan, loc, np.nan])
            args = (est[0], loc, est[1])
            return stats.kstest(rvs,'pareto',args)[0]

        #locest = optimize.fmin(pareto_ks, rvsmin*0.7, (rvs,))
        maxind = min(np.floor(self.nobs*0.95).astype(int), self.nobs-10)
        res = []
        for trimidx in range(self.nobs//2, maxind):
            xmin = loc = rvs[trimidx]
            res.append([trimidx, pareto_ks(loc-1e-10, rvs[trimidx:])])
        res = np.array(res)
        bestidx = res[np.argmin(res[:,1]),0].astype(int)
        print(bestidx)
        locest = rvs[bestidx]

        est = stats.pareto.fit_fr(rvs[bestidx:], 1., frozen=[np.nan, locest, np.nan])
        args = (est[0], locest, est[1])
        return args

    def fit_ks1(self):
        '''fit Pareto with nested optimization

        originally published on stackoverflow

        '''
        rvs = self.endog
        rvsmin = rvs.min()

        def pareto_ks(loc, rvs):
            #start_scale = rvs.min() - loc # not used yet
            est = stats.pareto.fit_fr(rvs, 1., frozen=[np.nan, loc, np.nan])
            args = (est[0], loc, est[1])
            return stats.kstest(rvs,'pareto',args)[0]

        #locest = optimize.fmin(pareto_ks, rvsmin*0.7, (rvs,))
        locest = optimize.fmin(pareto_ks, rvsmin - 1.5, (rvs,))
        est = stats.pareto.fit_fr(rvs, 1., frozen=[np.nan, locest, np.nan])
        args = (est[0], locest[0], est[1])
        return args

#y = stats.pareto.rvs(1, loc=10, scale=2, size=nobs)
y = stats.pareto.rvs(1, loc=0, scale=2, size=nobs)


par_start_params = np.array([1., 9., 2.])

mod_par = MyPareto(y)
mod_par.start_params = np.array([1., 10., 2.])
mod_par.start_params = np.array([1., -9., 2.])
mod_par.fixed_params = None

fixdf = np.nan * np.ones(mod_par.start_params.shape)
fixdf[1] = 9.9
#fixdf[2] = 2.
fixone = 0
if fixone:
    mod_par.fixed_params = fixdf
    mod_par.fixed_paramsmask = np.isnan(fixdf)
    mod_par.start_params = mod_par.start_params[mod_par.fixed_paramsmask]
    mod_par.df_model = 2
    mod_par.df_resid = mod_par.endog.shape[0] - mod_par.df_model
    mod_par.data.xnames = ['shape', 'scale']
else:
    mod_par.fixed_params = None
    mod_par.fixed_paramsmask = None
    mod_par.df_model = 3
    mod_par.df_resid = mod_par.endog.shape[0] - mod_par.df_model
    mod_par.data.xnames = ['shape', 'loc', 'scale']

res_par = mod_par.fit(start_params=mod_par.start_params, method='nm', maxfun=10000, maxiter=5000)
#res_par2 = mod_par.fit(start_params=res_par.params, method='newton', maxfun=10000, maxiter=5000)

res_parks = mod_par.fit_ks1()

print(res_par.params)
#print res_par2.params
print(res_parks)

print(res_par.params[1:].sum(), sum(res_parks[1:]), mod_par.endog.min())

#start new model, so we do not get two result instances with the same model instance
mod_par = MyPareto(y)
mod_par.fixed_params = fixdf
mod_par.fixed_paramsmask = np.isnan(fixdf)
mod_par.df_model = mod_par.fixed_paramsmask.sum()
mod_par.df_resid = mod_par.endog.shape[0] - mod_par.df_model
#mod_par.data.xnames = np.array(['shape', 'loc', 'scale'])[mod_par.fixed_paramsmask].tolist() # works also
mod_par.data.xnames = [name for (name, incl) in zip(['shape', 'loc', 'scale'], mod_par.fixed_paramsmask) if incl]

res_par3 = mod_par.start_params = par_start_params[mod_par.fixed_paramsmask]
res5 = mod_par.fit(start_params=mod_par.start_params)
##res_parks2 = mod_par.fit_ks()
##
##res_parkst = mod_par.fit_ks1_trim()
##print res_parkst

print(res5.summary())
print(res5.t_test([[1,0]]))

'''
0.0686702747648
0.0164150896481
0.128121386381
[ 0.10370428  0.09921315  0.09676723  0.10457413  0.10201618  0.89964496]
(array(0.0), array(1.4552599885729831), array(0.0), array(2.5072143354058238))
(array(0.0), array(1.6666666666666667), array(0.0), array(6.0))
repr(start_params) array([ 0.10370428,  0.09921315,  0.09676723,  0.10457413,  0.10201618,
        0.89964496,  6.39309417,  0.12812139])
Optimization terminated successfully.
         Current function value: -679.951339
         Iterations: 398
         Function evaluations: 609

estimation results t-dist
[ 0.10400826  0.10111893  0.09725133  0.10507788  0.10086163  0.8996041
  4.72131318  0.09825355]
[ 0.00365493  0.00356149  0.00349329  0.00362333  0.003732    0.00362716
  0.7232824   0.00388829]
repr(start_params) array([ 0.10400826,  0.10111893,  0.09725133,  0.10507788,  0.10086163,
        0.8996041 ,  4.72131318,  0.09825355])
Optimization terminated successfully.
         Current function value: -679.950443
         Iterations 3
using Newton
[ 0.10395383  0.10106762  0.09720665  0.10503384  0.10080599  0.89954546
  4.70918964  0.09815885]
[ 0.00365299  0.00355968  0.00349147  0.00362166  0.00373015  0.00362533
  0.72014031  0.00388434]
()
[ 0.09992709  0.09786601  0.09387356  0.10229919  0.09756623  0.85466272
  4.60459182  0.09661986]
[ 0.11308292  0.10828401  0.1028508   0.11268895  0.10934726  0.94462721
  7.15412655  0.13452746]
repr(start_params) array([ 1.,  2.])
Warning: Maximum number of function evaluations has been exceeded.
>>> res_par.params
array([  7.42705803e+152,   2.17339053e+153])

>>> mod_par.loglike(mod_par.start_params)
-1085.1993430947232
>>> np.log(mod_par.pdf(*mod_par.start_params))
0.69314718055994529
>>> mod_par.loglike(mod_par.start_params)
-1085.1993430947232
>>> np.log(stats.pareto.pdf(y[0],*mod_par.start_params))
-4.6414308627431353
>>> mod_par.loglike(mod_par.start_params)
-1085.1993430947232
>>> mod_par.nloglikeobs(mod_par.start_params)[0]
0.29377232943845044
>>> mod_par.start_params
array([ 1.,  2.])
>>> np.log(stats.pareto.pdf(y[0],1,9.5,2))
-1.2806918394368461
>>> mod_par.fixed_params= None
>>> mod_par.nloglikeobs(np.array([1., 10., 2.]))[0]
0.087533156771285828
>>> y[0]
12.182956907488885

>>> mod_par.endog[0]
12.182956907488885
>>> np.log(stats.pareto.pdf(y[0],1,10,2))
-0.86821349410251702
>>> np.log(stats.pareto.pdf(y[0],1.,10.,2.))
-0.86821349410251702
>>> stats.pareto.pdf(y[0],1.,10.,2.)
0.41970067762301644
>>> mod_par.loglikeobs(np.array([1., 10., 2.]))[0]
-0.087533156771285828
>>>
'''

'''
>>> mod_par.nloglikeobs(np.array([1., 10., 2.]))[0]
0.86821349410251691
>>> np.log(stats.pareto.pdf(y,1.,10.,2.)).sum()
-2627.9403758026938
'''


#'''
#0.0686702747648
#0.0164150896481
#0.128121386381
#[ 0.10370428  0.09921315  0.09676723  0.10457413  0.10201618  0.89964496]
#(array(0.0), array(1.4552599885729827), array(0.0), array(2.5072143354058203))
#(array(0.0), array(1.6666666666666667), array(0.0), array(6.0))
#repr(start_params) array([ 0.10370428,  0.09921315,  0.09676723,  0.10457413,  0.10201618,
#        0.89964496,  6.39309417,  0.12812139])
#Optimization terminated successfully.
#         Current function value: -679.951339
#         Iterations: 398
#         Function evaluations: 609
#
#estimation results t-dist
#[ 0.10400826  0.10111893  0.09725133  0.10507788  0.10086163  0.8996041
#  4.72131318  0.09825355]
#[ 0.00365493  0.00356149  0.00349329  0.00362333  0.003732    0.00362716
#  0.72325227  0.00388822]
#repr(start_params) array([ 0.10400826,  0.10111893,  0.09725133,  0.10507788,  0.10086163,
#        0.8996041 ,  4.72131318,  0.09825355])
#Optimization terminated successfully.
#         Current function value: -679.950443
#         Iterations 3
#using Newton
#[ 0.10395383  0.10106762  0.09720665  0.10503384  0.10080599  0.89954546
#  4.70918964  0.09815885]
#[ 0.00365299  0.00355968  0.00349147  0.00362166  0.00373015  0.00362533
#  0.72014669  0.00388436]
#()
#[ 0.09992709  0.09786601  0.09387356  0.10229919  0.09756623  0.85466272
#  4.60459182  0.09661986]
#[ 0.11308292  0.10828401  0.1028508   0.11268895  0.10934726  0.94462721
#  7.15412655  0.13452746]
#repr(start_params) array([ 1.,  2.])
#Warning: Maximum number of function evaluations has been exceeded.
#repr(start_params) array([  3.06504406e+302,   3.29325579e+303])
#
#>>> mod_par.fixed_params
#array([ NaN,  10.,  NaN])
#>>> mod_par.start_params
#array([ 1.,  2.])
#
#
#>>> stats.pareto.fit_fr(y, 1., frozen=[np.nan, 10., np.nan])
#array([ 1.0346268 ,  2.00184808])
#
#>>> stats.pareto.fit_fr(y, frozen=[np.nan, 10., np.nan])
#array([ 1.03463526,  2.00184809])
#>>> stats.pareto.pdf(y, 1.03463526, 10, 2.00184809).sum()
#173.33947284555239
#
#>>> mod_par.loglike((1.03463526, 10, 2.00184809))
#-962.21623668859741
#>>> np.log(stats.pareto.pdf(y, 1.03463526, 10, 2.00184809)).sum()
#-inf
#>>> np.log(stats.pareto.pdf(y, 1.03463526, 9, 2.00184809)).sum()
#-3074.5947476137271
#>>> np.log(stats.pareto.pdf(y, 1.03463526, 10., 2.00184809)).sum()
#-inf
#>>> np.log(stats.pareto.pdf(y, 1.03463526, 9.9, 2.00184809)).sum()
#-2677.3867091635661
#>>> y.min()
#12.001848089426717
#>>> np.log(stats.pareto.pdf(y, 1.03463526, loc=9.9, scale=2.00184809)).sum()
#-2677.3867091635661
#>>> np.log(stats.pareto.pdf(y, 1.03463526, loc=10., scale=2.00184809)).sum()
#-inf
#>>> stats.pareto.logpdf(y, 1.03463526, loc=10., scale=2.00184809).sum()
#-inf
#>>> stats.pareto.logpdf(y, 1.03463526, loc=9.99, scale=2.00184809).sum()
#-2631.6120098202355
#>>> mod_par.loglike((1.03463526, 9.99, 2.00184809))
#-963.2513896113644
#>>> maxabs(y, mod_par.endog)
#0.0
#
#>>> stats.pareto.a
#1.0
#
#>>> b, loc, scale = (1.03463526, 9.99, 2.00184809)
#>>> (1-loc)/scale
#-4.4908502522786327
#
#>>> lb = scale + loc
#>>> lb
#11.991848090000001
#>>> (lb-loc)/scale == 1
#False
#>>> (lb-loc)/scale
#1.0000000000000004
#>>>
#'''

'''
repr(start_params) array([  1.,  10.,   2.])
Optimization terminated successfully.
         Current function value: 2626.436870
         Iterations: 102
         Function evaluations: 210
Optimization terminated successfully.
         Current function value: 0.016555
         Iterations: 16
         Function evaluations: 35
[  1.03482659  10.00737039   1.9944777 ]
(1.0596088578825995, 9.9043376069230007, 2.0975104813987118)
>>> 9.9043376069230007 + 2.0975104813987118
12.001848088321712
>>> y.min()
12.001848089426717

'''

'''
0.0686702747648
0.0164150896481
0.128121386381
[ 0.10370428  0.09921315  0.09676723  0.10457413  0.10201618  0.89964496]
(array(0.0), array(1.4552599885729829), array(0.0), array(2.5072143354058221))
(array(0.0), array(1.6666666666666667), array(0.0), array(6.0))
repr(start_params) array([ 0.10370428,  0.09921315,  0.09676723,  0.10457413,  0.10201618,
        0.89964496,  6.39309417,  0.12812139])
Optimization terminated successfully.
         Current function value: -679.951339
         Iterations: 398
         Function evaluations: 609

estimation results t-dist
[ 0.10400826  0.10111893  0.09725133  0.10507788  0.10086163  0.8996041
  4.72131318  0.09825355]
[ 0.00365493  0.00356149  0.00349329  0.00362333  0.003732    0.00362716
  0.72329352  0.00388832]
repr(start_params) array([ 0.10400826,  0.10111893,  0.09725133,  0.10507788,  0.10086163,
        0.8996041 ,  4.72131318,  0.09825355])
Optimization terminated successfully.
         Current function value: -679.950443
         Iterations 3
using Newton
[ 0.10395383  0.10106762  0.09720665  0.10503384  0.10080599  0.89954546
  4.70918964  0.09815885]
[ 0.00365299  0.00355968  0.00349147  0.00362166  0.00373015  0.00362533
  0.7201488   0.00388437]
()
[ 0.09992709  0.09786601  0.09387356  0.10229919  0.09756623  0.85466272
  4.60459182  0.09661986]
[ 0.11308292  0.10828401  0.1028508   0.11268895  0.10934726  0.94462721
  7.15412655  0.13452746]
repr(start_params) array([ 1.,  9.,  2.])
Optimization terminated successfully.
         Current function value: 2636.129089
         Iterations: 147
         Function evaluations: 279
Optimization terminated successfully.
         Current function value: 0.016555
         Iterations: 16
         Function evaluations: 35
[  0.84856418  10.2197801    1.78206799]
(1.0596088578825995, 9.9043376069230007, 2.0975104813987118)
12.0018480891 12.0018480883 12.0018480894
repr(start_params) array([ 1.,  2.])
Warning: Desired error not necessarily achieveddue to precision loss
         Current function value: 2643.549907
         Iterations: 2
         Function evaluations: 13
         Gradient evaluations: 12
>>> res_parks2 = mod_par.fit_ks()
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2642.465273
         Iterations: 92
         Function evaluations: 172
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2636.639863
         Iterations: 73
         Function evaluations: 136
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2631.568778
         Iterations: 75
         Function evaluations: 133
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2627.821044
         Iterations: 75
         Function evaluations: 135
repr(start_params) array([ 1.,  2.])
Warning: Maximum number of function evaluations has been exceeded.
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2631.568778
         Iterations: 75
         Function evaluations: 133
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.431596
         Iterations: 58
         Function evaluations: 109
repr(start_params) array([ 1.,  2.])
Warning: Maximum number of function evaluations has been exceeded.
repr(start_params) array([ 1.,  2.])
Warning: Maximum number of function evaluations has been exceeded.
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.737426
         Iterations: 60
         Function evaluations: 109
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2627.821044
         Iterations: 75
         Function evaluations: 135
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.471666
         Iterations: 48
         Function evaluations: 94
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2627.196314
         Iterations: 66
         Function evaluations: 119
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.578538
         Iterations: 56
         Function evaluations: 103
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.471666
         Iterations: 48
         Function evaluations: 94
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.651702
         Iterations: 67
         Function evaluations: 122
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.737426
         Iterations: 60
         Function evaluations: 109
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.613505
         Iterations: 73
         Function evaluations: 141
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.578538
         Iterations: 56
         Function evaluations: 103
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.632218
         Iterations: 64
         Function evaluations: 119
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.651702
         Iterations: 67
         Function evaluations: 122
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.622789
         Iterations: 63
         Function evaluations: 114
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.613505
         Iterations: 73
         Function evaluations: 141
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.627465
         Iterations: 59
         Function evaluations: 109
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.632218
         Iterations: 64
         Function evaluations: 119
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.625104
         Iterations: 59
         Function evaluations: 108
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.629829
         Iterations: 66
         Function evaluations: 118
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.632218
         Iterations: 64
         Function evaluations: 119
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.632218
         Iterations: 64
         Function evaluations: 119
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.628642
         Iterations: 67
         Function evaluations: 122
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.631023
         Iterations: 68
         Function evaluations: 129
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.630430
         Iterations: 57
         Function evaluations: 108
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.629598
         Iterations: 60
         Function evaluations: 112
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.630430
         Iterations: 57
         Function evaluations: 108
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.630130
         Iterations: 65
         Function evaluations: 122
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.629536
         Iterations: 62
         Function evaluations: 111
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.630130
         Iterations: 65
         Function evaluations: 122
repr(start_params) array([ 1.,  2.])
Optimization terminated successfully.
         Current function value: 2626.629984
         Iterations: 67
         Function evaluations: 123
Optimization terminated successfully.
         Current function value: 0.016560
         Iterations: 18
         Function evaluations: 38
>>> res_parks2
(1.0592352626264809, 9.9051580457572399, 2.0966900385041591)
>>> res_parks
(1.0596088578825995, 9.9043376069230007, 2.0975104813987118)
>>> res_par.params
array([  0.84856418,  10.2197801 ,   1.78206799])
>>> np.sqrt(np.diag(mod_par.hessian(res_par.params)))
array([ NaN,  NaN,  NaN])
>>> mod_par.hessian(res_par.params
... )
array([[ NaN,  NaN,  NaN],
       [ NaN,  NaN,  NaN],
       [ NaN,  NaN,  NaN]])
>>> mod_par.hessian(res_parks)
array([[ NaN,  NaN,  NaN],
       [ NaN,  NaN,  NaN],
       [ NaN,  NaN,  NaN]])

>>> mod_par.hessian(np.array(res_parks))
array([[ NaN,  NaN,  NaN],
       [ NaN,  NaN,  NaN],
       [ NaN,  NaN,  NaN]])
>>> mod_par.fixed_params
array([        NaN,  9.90510677,         NaN])
>>> mod_par.fixed_params=None
>>> mod_par.hessian(np.array(res_parks))
array([[-890.48553491,           NaN,           NaN],
       [          NaN,           NaN,           NaN],
       [          NaN,           NaN,           NaN]])
>>> mod_par.loglike(np.array(res_parks))
-2626.6322080820569
>>> mod_par.bsejac
Traceback (most recent call last):
  [...]
AttributeError: 'MyPareto' object has no attribute 'bsejac'

>>> hasattr(mod_par, 'start_params')
True
>>> mod_par.start_params
array([ 1.,  2.])
>>> stats.pareto.stats(1., 9., 2., moments='mvsk')
(array(1.#INF), array(1.#INF), array(1.#QNAN), array(1.#QNAN))
>>> stats.pareto.stats(1., 8., 2., moments='mvsk')
(array(1.#INF), array(1.#INF), array(1.#QNAN), array(1.#QNAN))
>>> stats.pareto.stats(1., 8., 1., moments='mvsk')
(array(1.#INF), array(1.#INF), array(1.#QNAN), array(1.#QNAN))
>>> stats.pareto.stats(1., moments='mvsk')
(array(1.#INF), array(1.#INF), array(1.#QNAN), array(1.#QNAN))
>>> stats.pareto.stats(0.5, moments='mvsk')
(array(1.#INF), array(1.#INF), array(1.#QNAN), array(1.#QNAN))
>>> stats.pareto.stats(2, moments='mvsk')
(array(2.0), array(1.#INF), array(1.#QNAN), array(1.#QNAN))
>>> stats.pareto.stats(10, moments='mvsk')
(array(1.1111111111111112), array(0.015432098765432098), array(2.8110568859997356), array(14.828571428571429))
>>> stats.pareto.rvs(10, size=10)
array([ 1.07716265,  1.18977526,  1.07093   ,  1.05157081,  1.15991232,
        1.31015589,  1.06675107,  1.08082475,  1.19501243,  1.34967158])
>>> r = stats.pareto.rvs(10, size=1000)

>>> import matplotlib.pyplot as plt
>>> plt.hist(r)
(array([962,  32,   3,   2,   0,   0,   0,   0,   0,   1]), array([ 1.00013046,  1.3968991 ,  1.79366773,  2.19043637,  2.587205  ,
        2.98397364,  3.38074227,  3.77751091,  4.17427955,  4.57104818,
        4.96781682]), <a list of 10 Patch objects>)
>>> plt.show()

'''
