>h.2SrSSKrSSKJr SSKJr SSKJ r J r SSK J r SSK J r \R"S 5S\R4S jr\R"S 5\R"S 5- S4S jrS\R$"S 5\R"S5-- S4SjrS\R$"S 5\R"S5-- 4Sjr"SS5r\"5r"SS5r\"5rg)a Support and standalone functions for Robust Linear Models References ---------- PJ Huber. 'Robust Statistics' John Wiley and Sons, Inc., New York, 1981. R Venables, B Ripley. 'Modern Applied Statistics in S' Springer, New York, 2002. C Croux, PJ Rousseeuw, 'Time-efficient algorithms for two highly robust estimators of scale' Computational statistics. Physica, Heidelberg, 1992. N)norm)tools) array_like float_like)norms)_qn?c2[USSS9n[US5nUR(dSnON[U5(a2Ub[R "X0U5nO#U"UR 55nO [US5n[R"X- 5U- nUR(d_UbURS:Xa[R$[UR5nURU5 [R"U5$[R"XRS9$) aZ The Median Absolute Deviation along given axis of an array Parameters ---------- a : array_like Input array. c : float, optional The normalization constant. Defined as scipy.stats.norm.ppf(3/4.), which is approximately 0.6745. axis : int, optional The default is 0. Can also be None. center : callable or float If a callable is provided, such as the default `np.median` then it is expected to be called center(a). The axis argument will be applied via np.apply_over_axes. Otherwise, provide a float. Returns ------- mad : float `mad` = median(abs(`a` - center))/`c` aNndimcgcenterraxis)rrsizecallablenpapply_over_axesravelabsrnanlistshapepopemptymedian)r rrr center_valerrrs kC:\Users\julio\OneDrive\Documentos\Trabajo\Ideas Frescas\venv\Lib\site-packages\statsmodels/robust/scale.pymadr"s. 1c%A1cA 66 &    ++Ft>> import numpy as np >>> import statsmodels.api as sm >>> chem_data = np.array([2.20, 2.20, 2.4, 2.4, 2.5, 2.7, 2.8, 2.9, 3.03, ... 3.03, 3.10, 3.37, 3.4, 3.4, 3.4, 3.5, 3.6, 3.7, 3.7, 3.7, 3.7, ... 3.77, 5.28, 28.95]) >>> sm.robust.scale.huber(chem_data) (array(3.2054980819923693), array(0.67365260010478967)) NcXlX0lX lX@lS[R "U5-S- nXQS-SU- --SU-[R "U5-- UlgNr-r)rmaxitertolrGaussiancdfpdfgamma)selfrrKrJrtmps r!__init__Huber.__init__sZ  (,,q/!A%6QW--A Q0GG r#ct[R"U5nUc)URSS- n[R"XS9nSnOURSnUnSnUc [ XS9nOUn[ R "XtUR5n[ R "X$UR5nURXX$Xe5$)a Compute Huber's proposal 2 estimate of scale, using an optional initial value of scale and an optional estimate of mu. If mu is supplied, it is not reestimated. Parameters ---------- a : ndarray 1d array mu : float or None, optional If the location mu is supplied then it is not reestimated. Default is None, which means that it is estimated. initscale : float or None, optional A first guess on scale. If initscale is None then the standardized median absolute deviation of a is used. Notes ----- `Huber` minimizes the function sum(psi((a[i]-mu)/scale)**2) as a function of (mu, scale), where psi(x) = np.clip(x, -self.c, self.c) rrrTF)rasarrayrrr"r unsqueeze_estimate_both)rPr mu initscalerr?est_muscales r!__call__Huber.__call__s6 JJqM : QA1(BF ABF  %EEQWW5 __Rqww /""1RvAAr#c Z[UR5GHznU(aURcV[R"XUR U-- X0R U--5R U5URU- nOI[R"XURXCURUR5nOUR5n[R"XUR5n[R"[R"X- U- 5UR 5n U R U5n [R "XU- S--U5n X`R -URUU - UR S--- n [R""X- 5n [R"XUR5n [R$"[R"[R"X-- 5XR-55n[R$"[R"[R"X8- 5XR-55nU(aU(dUnU nGM[UR5U R54s $ ['SUR-5e)a, Estimate scale and location simultaneously with the following pseudo_loop: while not_converged: mu, scale = estimate_location(a, scale, mu), estimate_scale(a, scale, mu) where estimate_location is an M-estimator and estimate_scale implements the check used in Section 5.5 of Venables & Ripley r-zJjoint estimation of location and scale failed to converge in %d iterations)rangerJrrcliprsumrrestimate_locationrKr)rrV less_equalrrOsqrtallr')rPr r[rXrrZr?_nmusubsetcard scale_num scale_denomnscaletest1test2s r!rWHuber._estimate_bothst||$A99$ DFFUN2B%4G#d)''$-( 11$))Tt||TXXC jjl//#QWW5C]]26616U*:#;TVVDF::d#DvSQ6=Ijj.AGGDMD,@DFFaK+OOKWWY45F__V177;FFF bffU^4fxx6GHEFF bffRX.0ABEe{{}fnn&666Q%R +-1\\ :  r#)rrOrJrrK)g?:0yE>N)NNr) __name__ __module__ __qualname____firstlineno____doc__rRr\rW__static_attributes__r#r!rFrFs<H+BZ7 r#rFc(\rSrSrSrSSjrSrSrg) HuberScalei@a6 Huber's scaling for fitting robust linear models. Huber's scale is intended to be used as the scale estimate in the IRLS algorithm and is slightly different than the `Huber` class. Parameters ---------- d : float, optional d is the tuning constant for Huber's scale. Default is 2.5 tol : float, optional The convergence tolerance maxiter : int, optiona The maximum number of iterations. The default is 30. Methods ------- call Return's Huber's scale computed as below Notes ----- Huber's scale is the iterative solution to scale_(i+1)**2 = 1/(n*h)*sum(chi(r/sigma_i)*sigma_i**2 where the Huber function is chi(x) = (x**2)/2 for \|x\| < d chi(x) = (d**2)/2 for \|x\| >= d and the Huber constant h = (n-p)/n*(d**2 + (1-d**2)* scipy.stats.norm.cdf(d) - .5 - d*sqrt(2*pi)*exp(-0.5*d**2) c(XlX lX0lgN)drKrJ)rPr}rKrJs r!rRHuberScale.__init__ds r#c n^^^ UU- TRS-STRS-- [R"TR5--S- TR[R"S[R -5- [R "STRS--5-- -n[T5nUU4Sjm UUU 4Sjn[RU/nSn[R"XxS- Xx- 5TR:aUTR:a[R"SX$-- [R"U"US55-USS--5n URU 5 US- n[R"XxS- Xx- 5TR:aUTR:aMUS$)Nr-rg?gct>[R"[R"TU- 5TR5$r|)rlessrr})xresidrPs r!rh#HuberScale.__call__..subsetvs%77266%!),dff5 5r#cj>T"U5TU- S--S- ST"U5- TRS-S- --$rI)r})srrPrhs r!chi HuberScale.__call__..chiysE!9 a//!3q6!9}! a7 r#)r}rLrMrrdpiexpr"infrrKrJraappend) rPdf_residnobsrr@rr scalehistniterrlrhs ` ` @r!r\HuberScale.__call__is  ! tvv{?hll466&::;&&BGGAI./"&&! 9K2LLM   J 6  VVQK  FF9QY')*:: ;dhh F $WW8&&Yr]+,-B-1$%F   V $ QJE FF9QY')*:: ;dhh F $}r#)r}rJrKN)g@rprq)rrrsrtrurvrRr\rwrxr#r!rzrz@s!F $r#rz)rvnumpyr scipy.statsrrLstatsmodels.toolsrstatsmodels.tools.validationrrrr ppfrr"r,rdr8rDrFhuberrz hubers_scalerxr#r!rs (#?\\' "299*%Z\\% 8<<#6 6Q:@rwwqzHLL$778q'T X\\%%889@K K \ MM`| r#