M/Ph] dZddlmZddlZddlmZmZmZej ej j _ ej ej j _ dZd8dZd8dZdZd Zd9d Zd9dZ d:dZeej j_eej j_eej j_eej j_eej j_eej j_d;dZdifdZd4 EQJJv  !C%5!!A $&[Q$&[ )E u 6v FFtz!#d###au o55s AAA4c|t|jddgddg\}}t|}|dkr&t|dr||}n1||jkrt d|d|j|z zz }|||fz}d |vrtj|d }t||jd zkrt d tt|D]P} t|| tj r.|| j d kr||  || <Q|tj}tj|tj|}nd }t#j|j|tj||fdS)aestimate distribution parameters by MLE taking some parameters as fixed Parameters ---------- data : ndarray, 1d data for which the distribution parameters are estimated, args : list ? check starting values for optimization kwds : - 'frozen' : array_like values for frozen distribution parameters and, for elements with np.nan, the corresponding parameter will be estimated Returns ------- argest : ndarray estimated parameters Examples -------- generate random sample >>> np.random.seed(12345) >>> x = stats.gamma.rvs(2.5, loc=0, scale=1.2, size=200) estimate all parameters >>> stats.gamma.fit(x) array([ 2.0243194 , 0.20395655, 1.44411371]) >>> stats.gamma.fit_fr(x, frozen=[np.nan, np.nan, np.nan]) array([ 2.0243194 , 0.20395655, 1.44411371]) keep loc fixed, estimate shape and scale parameters >>> stats.gamma.fit_fr(x, frozen=[np.nan, 0.0, np.nan]) array([ 2.45603985, 1.27333105]) keep loc and scale fixed, estimate shape parameter >>> stats.gamma.fit_fr(x, frozen=[np.nan, 0.0, 1.0]) array([ 3.00048828]) >>> stats.gamma.fit_fr(x, frozen=[np.nan, 0.0, 1.2]) array([ 2.57792969]) estimate only scale parameter for fixed shape and loc >>> stats.gamma.fit_fr(x, frozen=[2.5, 0.0, np.nan]) array([ 1.25087891]) Notes ----- self is an instance of a distribution class. This can be attached to scipy.stats.distributions.rv_continuous *Todo* * check if docstring is correct * more input checking, args is list ? might also apply to current fit method rr?rrzToo many input arguments.)rBfrozenr z%Incorrect number of frozen arguments.rN)r<disp)rgetr6hasattrrnumargsr1r r4range isinstancendarraysizeitemastypefloat64rrfminr?ravel) rdatar<kwdsloc0scale0Nargx0r:ns rfit_frrXst5'"2C:>>LD& t99D qyyWT;//y ^^D ! !   4555  T)** T6N "4$x.)) v;;$,q. ( (DEE E3v;;'' 1 1fQi44119L9L &q  0 0F1I]]2:..F(2,,rx//0BB =rhtnnf-A 7 7 77rrFcfd}nfd}| jzz}| jzz}|r&j|g|Rdj|g|Rdz } nd} tj||||d| z S)acalculate expected value of a function with respect to the distribution location and scale only tested on a few examples Parameters ---------- all parameters are keyword parameters fn : function (default: identity mapping) Function for which integral is calculated. Takes only one argument. args : tuple argument (parameters) of the distribution lb, ub : numbers lower and upper bound for integration, default is set to the support of the distribution conditional : bool (False) If true then the integral is corrected by the conditional probability of the integration interval. The return value is the expectation of the function, conditional on being in the given interval. Returns ------- expected value : float Notes ----- This function has not been checked for it's behavior when the integral is not finite. The integration behavior is inherited from scipy.integrate.quad. Nc.|j|g|RdzSNrrpdfrr<rrrs rfunzexpect..funIs,XTXa===S==== =rc@|j|g|RdzSr\r^rr<fnrrrs rrazexpect..funLs42a55!ADAAEAAAA Arr]rB)r<r)rr!sfrquad rrdr<rrlbub conditionalrainvfacs `` `` rexpectrl*s< z > > > > > > > > B B B B B B B B z 46E> ! z 46E> !$'":T::#U:::DGB#r2%) + + ++, ..4 55rcfd}nfd}|' jdg|R}n5#t$r j}Yn"wxYwtj|z dzz }|' jdg|R}n5#t$r j}Yn"wxYwt j|z dzz }|rj|g|Rj|g|Rz } nd} tj||||dd | z S) acalculate expected value of a function with respect to the distribution location and scale only tested on a few examples Parameters ---------- all parameters are keyword parameters fn : function (default: identity mapping) Function for which integral is calculated. Takes only one argument. args : tuple argument (parameters) of the distribution lb, ub : numbers lower and upper bound for integration, default is set using quantiles of the distribution, see Notes conditional : bool (False) If true then the integral is corrected by the conditional probability of the integration interval. The return value is the expectation of the function, conditional on being in the given interval. Returns ------- expected value : float Notes ----- This function has not been checked for it's behavior when the integral is not finite. The integration behavior is inherited from scipy.integrate.quad. The default limits are lb = self.ppf(1e-9, *args), ub = self.ppf(1-1e-9, *args) For some heavy tailed distributions, 'alpha', 'cauchy', 'halfcauchy', 'levy', 'levy_l', and for 'ncf', the default limits are not set correctly even when the expectation of the function is finite. In this case, the integration limits, lb and ub, should be chosen by the user. For example, for the ncf distribution, ub=1000 works in the examples. There are also problems with numerical integration in some other cases, for example if the distribution is very concentrated and the default limits are too large. Nc2|zzj|g|RzSN_pdfr`s rrazexpect_v2..funs*!E'M949Q#6#6#6#66 6rcD|zzj|g|RzSrorprcs rrazexpect_v2..funs42cAeGm$$YTYq%84%8%8%88 8rg& .>rBgv?i)r<limitr) ppfr1rrr!r _sfrrfrgs `` `` r expect_v2rv[s^ z 7 7 7 7 7 7 7 7 9 9 9 9 9 9 9 9 z $&&&&BB   BBB "s(SY/ 0 0 z &(4(((BB   BBB "s(SY/ 0 0"#d###hdhr&84&8&8&88 >#r2%) 6 6 667 99? @@s)==!A00BBcd}d}fd} nfd} j|j}n|z }|j}n|z }|r!j|gRj|dzgRz } nd} d} jd gRjd gR} } t t | | |} t t || |} tj| | dzj }tj | |} d }| j z}d }||krG|j kr<||kr6| |}| |z } |j z }|dz }||kr|j kr||k6jd krYd }| j z }||krG|j kr<||kr6| |}| |z } |j z}|dz }||kr|j kr||k6||krtd | | z S)acalculate expected value of a function with respect to the distribution for discrete distribution Parameters ---------- (self : distribution instance as defined in scipy stats) fn : function (default: identity mapping) Function for which integral is calculated. Takes only one argument. args : tuple argument (parameters) of the distribution optional keyword parameters lb, ub : numbers lower and upper bound for integration, default is set to the support of the distribution, lb and ub are inclusive (ul<=k<=ub) conditional : bool (False) If true then the expectation is corrected by the conditional probability of the integration interval. The return value is the expectation of the function, conditional on being in the given interval (k such that ul<=k<=ub). Returns ------- expected value : float Notes ----- * function is not vectorized * accuracy: uses self.moment_tol as stopping criterium for heavy tailed distribution e.g. zipf(4), accuracy for mean, variance in example is only 1e-5, increasing precision (moment_tol) makes zipf very slow * suppnmin=100 internal parameter for minimum number of points to evaluate could be added as keyword parameter, to evaluate functions with non-monotonic shapes, points include integers in (-suppnmin, suppnmin) * uses maxcount=1000 limits the number of points that are evaluated to break loop for infinite sums (a maximum of suppnmin+1000 positive plus suppnmin+1000 negative integers are evaluated) dNc,|zj|gRzSro_pmf)rr<rrs rrazexpect_discrete..funs&cE949Q..... .rc>|zj|gRzSror{)rr<rdrrs rrazexpect_discrete..funs.2ae99YTYq040000 0rrrBrAgMbP?g+?g}Ô%ITrzsum did not converge) r2rr!re_ppfrr r arangeincsum moment_tolprint)rrdr<rrhrirjmaxcountsuppnminrarktotlowuppsuppdiffposcounts```` rexpect_discreters`HH z / / / / / / / / 1 1 1 1 1 1 1 1DND zf #X zf #X"T"""WTWRT%84%8%8%88 Cty&&&&  %(?$(?(?(?C c8)S!!2 & &C c(C  " % %C 9S#a% * *D &T  C D .C E "994$/11u7H7Hs3xx t  tx   "994$/11u7H7H  vzzDHnbyytdo555H;L;L3s88D 4KC 48OC QJE byytdo555H;L;L  x $%%% v:rryct|}tj|}t|D]R}tj||}||}||tjddg||<S|S)arun bootstrap for estimation of distribution parameters hard coded: only one shape parameter is allowed and estimated, loc=0 and scale=1 are fixed in the estimation Parameters ---------- sample : ndarray original sample data for bootstrap distr : distribution instance with fit_fr method nrepl : int number of bootstrap replications Returns ------- res : array (nrepl,) parameter estimates for all bootstrap replications )rKrArBrC)r6r zerosrHrandomrandintrXnan)sampledistrnreplnobsresiirvsindrs rdistfitbootstrapr%s}( v;;D (5//CEll==""4d"33 6N,,q"&#s);,<<B Jrc|d}t|}tj|}t |D]9}|j|fd|i|}||tjddg||<:|S)arun Monte Carlo for estimation of distribution parameters hard coded: only one shape parameter is allowed and estimated, loc=0 and scale=1 are fixed in the estimation Parameters ---------- sample : ndarray original sample data, in Monte Carlo only used to get nobs, distr : distribution instance with fit_fr method nrepl : int number of Monte Carlo replications Returns ------- res : array (nrepl,) parameter estimates for all Monte Carlo replications argrKrArBr)popr6r rrHrvsrXr) rrrdistkwdsrrrrrs r distfitmcrAs( ,,u  C v;;D (5//CEll== EIc 1 1 1 1 1,,q"&#s);,<<B Jr bootstrapc ,tdt|tdtzt|tjddg}t||dkr|}|}td|t fztd|d d d |d |z d td t j|d td| d t j | d ||z dzd }td|t j |t j |}td|zt|t j t dz|t j t dztd|zttjd||ttjd||td|ztdttj|d||fdS)acalculate and print(Bootstrap or Monte Carlo result Parameters ---------- sample : ndarray original sample data arg : float (for general case will be array) bres : ndarray parameter estimates from Bootstrap or Monte Carlo run kind : {'bootstrap', 'montecarlo'} output is printed for Mootstrap (default) or Monte Carlo Returns ------- None, currently only printing Notes ----- still a bit a mess because it is used for both Bootstrap and Monte Carlo made correction: reference point for bootstrap is estimated parameter not clear: I'm not doing any ddof adjustment in estimation of variance, do we need ddof>0 ? todo: return results and string instead of printing ztrue parameter valuez1MLE estimate of parameters using sample (nobs=%d)rArBrrz0%s distribution of parameter estimate (nrepl=%d)zmean = rfz, bias=median)axisz var and stdr z mse, rmsez&%s confidence interval (90%% coverage)g?gffffff?z;%s confidence interval (90%% coverage) normal approximationr]z8Kolmogorov-Smirnov test for normality of %s distributionz4 - estimated parameters, p-values not really correctnormN)rrrrXr rrrrrrsortfloorrrrtr isfkstest)rrbreskindargestargorigbmse bressorteds r printresultsr^ss> !!! #JJJ = EFFF \\&"&#s);\ < ? ?@@@@@r__main__) largenumberr montecarlorz Distribution: vonmises)gGz?)rrrKz nobs:ztrue parameterz1.23, loc=0, scale=1 unconstrainedrzwith fixed loc and scalerArBz Distribution: gamma)@rAg4@rz, loc=z, scale=zwith fixed locgammavonmises)rrAr)g?rArz wrong examplerxz Distribution:z Bootstrap)rrz MonteCarlo)rrr)rr)rro)NrYrrNNF)NrYrNNF)ry)r)1__doc__statsmodels.compat.pythonrnumpyr scipyrrrpi distributionsrrr!rr)r,r?rXrlrvr rv_continuous rv_discretebeta_gen poisson_genrrr__name__ examplecasesrrrrfitrrrrrrexr1rrrdictmcresrYrrrs  +*****,,,,,,,,,,#%%!# 6<<<<|1111h6666[7[7[7J.5.5.5.5bJ@J@J@J@d@D %llll\,2!(,3!)+1!()8&)7&,=) 8$':7A7A7A7At z===aaa@L $$ ())) G GD""4Qad"CCA E)T " " " E" # # # E( ) ) ) E/ " " " E%.$$Q'' ( ( ( E%.''2626262J'KK L L L E, - - - E%.''2632D'EE F F F F %&&& &S% A AD #3e$ ??A E)T " " " E" # # # ES:::#:::::: ; ; ; E/ " " " E%))A,,    E%,,q"&"&"&)A,BB C C C E, - - - E%,,q"&#s);,<< = = = E" # # # E%,,q"&#rv)>,?? @ @ @ @ : q !B W}} $S%% z  $S%%j))) D E YYs5tY <