>h9M SrSSKrSSKJrJr SSKJr SSKJ r SSK J r J r SSK Jr SS KJrJrJr SS KJr \"\R,\R.\R0\R2\R4\R6\R8\R:\R<S 9 rS r "S S5r!SSSSS\RD*\RD4SS4Sjr#SSSSS\RD*\RD4SS4Sjr$g)aa Univariate Kernel Density Estimators References ---------- Racine, Jeff. (2008) "Nonparametric Econometrics: A Primer," Foundation and Trends in Econometrics: Vol 3: No 1, pp1-88. http://dx.doi.org/10.1561/0800000009 https://en.wikipedia.org/wiki/Kernel_%28statistics%29 Silverman, B.W. Density Estimation for Statistics and Data Analysis. N) integratestats)kernels)cache_readonly) array_like float_like) bandwidths)forrtrevrtsilverman_transform) fast_linbin) gauepaunitribiwtriwcoscos2triccPUR g![a [S5ef=f)Nz!Call fit to fit the density first)density Exception ValueErrorselfs pC:\Users\julio\OneDrive\Documentos\Trabajo\Ideas Frescas\venv\Lib\site-packages\statsmodels/nonparametric/kde.py _checkisfitr(s)> ><==>s %c \rSrSrSrSrSSSSSSS \R*\R44S jr\ S 5r \ S 5r \ S 5r \ S5r \ S5rSrSrg) KDEUnivariate0aa Univariate Kernel Density Estimator. Parameters ---------- endog : array_like The variable for which the density estimate is desired. Notes ----- If cdf, sf, cumhazard, or entropy are computed, they are computed based on the definition of the kernel rather than the FFT approximation, even if the density is fit with FFT = True. `KDEUnivariate` is much faster than `KDEMultivariate`, due to its FFT-based implementation. It should be preferred for univariate, continuous data. `KDEMultivariate` also supports mixed data. See Also -------- KDEMultivariate kdensity, kdensityfft Examples -------- >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plt >>> nobs = 300 >>> np.random.seed(1234) # Seed random generator >>> dens = sm.nonparametric.KDEUnivariate(np.random.normal(size=nobs)) >>> dens.fit() >>> plt.plot(dens.cdf) >>> plt.show() c&[USSSS9Ulg)Nendogr T)ndim contiguous)rr$)rr$s r__init__KDEUnivariate.__init__UswQ4H rnormal_referenceTNr c [U[5(aX lO#SUl[U5(d [ US5nUR n U(a7US:wa Sn [ U 5eUb Sn [ U 5e[U UUUUUUUS9upnO[U UUUUUUUS9upnXl Xl X l [U"US9Ul X@RlUb-UR=RUR5-sl0UlU$)a Attach the density estimate to the KDEUnivariate class. Parameters ---------- kernel : str The Kernel to be used. Choices are: - "biw" for biweight - "cos" for cosine - "epa" for Epanechnikov - "gau" for Gaussian. - "tri" for triangular - "triw" for triweight - "uni" for uniform bw : str, float, callable The bandwidth to use. Choices are: - "scott" - 1.059 * A * nobs ** (-1/5.), where A is `min(std(x),IQR/1.34)` - "silverman" - .9 * A * nobs ** (-1/5.), where A is `min(std(x),IQR/1.34)` - "normal_reference" - C * A * nobs ** (-1/5.), where C is calculated from the kernel. Equivalent (up to 2 dp) to the "scott" bandwidth for gaussian kernels. See bandwidths.py - If a float is given, its value is used as the bandwidth. - If a callable is given, it's return value is used. The callable should take exactly two parameters, i.e., fn(x, kern), and return a float, where: * x - the clipped input data * kern - the kernel instance used fft : bool Whether or not to use FFT. FFT implementation is more computationally efficient. However, only the Gaussian kernel is implemented. If FFT is False, then a 'nobs' x 'gridsize' intermediate array is created. gridsize : int If gridsize is None, max(len(x), 50) is used. cut : float Defines the length of the grid past the lowest and highest values of x so that the kernel goes to zero. The end points are ``min(x) - cut * adjust * bw`` and ``max(x) + cut * adjust * bw``. adjust : float An adjustment factor for the bw. Bandwidth becomes bw * adjust. Returns ------- KDEUnivariate The instance fit, z user-givenbwrz)Only gaussian kernel is available for fftz#Weights are not implemented for fft)kernelr-adjustweightsgridsizeclipcut)h) isinstancestr bw_methodcallablerr$NotImplementedError kdensityfftkdensityrsupportr- kernel_switchr.r0sum_cache) rr.r-fftr0r1r/r3r2r$msgrgrids rfitKDEUnivariate.fitXs@ b#  N)DNB<<D)  A)#..";)#.. +! ! G2!)! ! G2  #F+b1 &    KK  7;;= 0   r)c ^ [U5 URm T Rc![R*[Rp!OT RupU 4SjnUR n[R X4n[U5nURn[SU5Vs/sH$n[R"X4US- XGUS9SPM& nn[R"U5$s snf)z Returns the cumulative distribution function evaluated at the support. Notes ----- Will not work if fit has not been called. cN>[R"TRX55$)N)npsqueezer)xskerns rfuncKDEUnivariate.cdf..funcs::dll101 1r)r argsr) rr.domainrGinfr<r_lenr$rangerquadcumsum) rabrLr<r1r$iprobsrKs @rcdfKDEUnivariate.cdfs D{{ ;; FF7BFFq;;DA 2,,%% #w< 1h' ' NN4Q% H K'  yy  s +C#cZ[U5 [R"UR5*$)zn Returns the hazard function evaluated at the support. Notes ----- Will not work if fit has not been called. )rrGlogsfrs r cumhazardKDEUnivariate.cumhazards! Dtwwr)c6[U5 SUR- $)zp Returns the survival function evaluated at the support. Notes ----- Will not work if fit has not been called. r )rr[rs rr_KDEUnivariate.sfs D488|r)c^[U5 U4SjnURmTRbURup#O [R*[Rp2UR n[ R"XX44S9S*$)z Returns the differential entropy evaluated at the support Notes ----- Will not work if fit has not been called. 1e-12 is added to each probability to ensure that log(0) is not called. c^>TRX5nU[R"US-5-$)Ng-q=)rrGr^)rIrJpdfrKs rentr#KDEUnivariate.entropy..entr s),,q$Ce ,, ,r)rNr)rr.rPrGrQr$rrU)rrgrWrXr$rKs @rentropyKDEUnivariate.entropysi D -{{ ;; ";;DAqFF7BFFq t9!<<r=r8floatr5r6r select_bandwidthrminrnTsethrPdot)rIr.r-r0r1r/r2r3retgridclip_xnobsqrArKrWrXrBkz_loz_high domain_maskdenss rr;r;4sT 1 Avv{ agJ ^^AQK!W 5F A q6DtR=''$- **W% w<3v; &NCS/ !..*+ KKM  "D|| 2a;  B    ( ( 5D !LB qqCH$A qqCH$A ;;qX &D d1d7m  A  IIbM {{ f4xAJ/ G+ GAa!eH 66!W  (DT2~Rxr)c 6[R"U5nU[R"XS:XS:5n[U"5n [ U5(a[ U"X 55nO9[ U[5(a[R"XU 5nO [US5nX%-n[U5n Uc[R"U S45nS[R"[R"U55-n[R"U5Xr-- n [R"U5Xr--n [R "X[#U5SS9upX- n[%X X5X-- n['U5n[)X$U5U-n[+U5nU(aUX4$UU4$)a Rosenblatt-Parzen univariate kernel density estimator Parameters ---------- x : array_like The variable for which the density estimate is desired. kernel : str ONLY GAUSSIAN IS CURRENTLY IMPLEMENTED. "bi" for biweight "cos" for cosine "epa" for Epanechnikov, default "epa2" for alternative Epanechnikov "gau" for Gaussian. "par" for Parzen "rect" for rectangular "tri" for triangular bw : str, float, callable The bandwidth to use. Choices are: - "scott" - 1.059 * A * nobs ** (-1/5.), where A is `min(std(x),IQR/1.34)` - "silverman" - .9 * A * nobs ** (-1/5.), where A is `min(std(x),IQR/1.34)` - "normal_reference" - C * A * nobs ** (-1/5.), where C is calculated from the kernel. Equivalent (up to 2 dp) to the "scott" bandwidth for gaussian kernels. See bandwidths.py - If a float is given, its value is used as the bandwidth. - If a callable is given, it's return value is used. The callable should take exactly two parameters, i.e., fn(x, kern), and return a float, where: * x - the clipped input data * kern - the kernel instance used weights : array or None WEIGHTS ARE NOT CURRENTLY IMPLEMENTED. Optional weights. If the x value is clipped, then this weight is also dropped. gridsize : int If gridsize is None, min(len(x), 512) is used. Note that the provided number is rounded up to the next highest power of 2. adjust : float An adjustment factor for the bw. Bandwidth becomes bw * adjust. clip : tuple Observations in x that are outside of the range given by clip are dropped. The number of observations in x is then shortened. cut : float Defines the length of the grid past the lowest and highest values of x so that the kernel goes to zero. The end points are -/+ cut*bw*{x.min() or x.max()} retgrid : bool Whether or not to return the grid over which the density is estimated. Returns ------- density : ndarray The densities estimated at the grid points. grid : ndarray, optional The grid points at which the density is estimated. Notes ----- Only the default kernel is implemented. Weights are not implemented yet. This follows Silverman (1982) with changes suggested by Jones and Lotwick (1984). However, the discretization step is replaced by linear binning of Fan and Marron (1994). This should be extended to accept the parts that are dependent only on the data to speed things up for cross-validation. References ---------- Fan, J. and J.S. Marron. (1994) `Fast implementations of nonparametric curve estimators`. Journal of Computational and Graphical Statistics. 3.1, 35-56. Jones, M.C. and H.W. Lotwick. (1984) `Remark AS R50: A Remark on Algorithm AS 176. Kernal Density Estimation Using the Fast Fourier Transform`. Journal of the Royal Statistical Society. Series C. 33.1, 120-2. Silverman, B.W. (1982) `Algorithm AS 176. Kernel density estimation using the Fast Fourier Transform. Journal of the Royal Statistical Society. 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