_Mh?dZgdZddlZddlmZmZddlmZddlmZddl m Z ddl m Z mZmZmZdd Zdd ZddZ ddZddZddZddZddZddZddZdS) zB Additional statistics functions with support for masked arrays. ) compare_medians_ms hdquantileshdmedianhdquantiles_sd idealfourths median_cihsmjcimquantiles_cimjrshtrimmed_mean_ciN)float64ndarray) MaskedArray) _mstats_basic)normbetatbinomg??g?Fcbd}tj|dt}tjtj|}| |jdkr||||}n:|jdkrtd|jztj|||||}tj |dS) a$ Computes quantile estimates with the Harrell-Davis method. The quantile estimates are calculated as a weighted linear combination of order statistics. Parameters ---------- data : array_like Data array. prob : sequence, optional Sequence of probabilities at which to compute the quantiles. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. var : bool, optional Whether to return the variance of the estimate. Returns ------- hdquantiles : MaskedArray A (p,) array of quantiles (if `var` is False), or a (2,p) array of quantiles and variances (if `var` is True), where ``p`` is the number of quantiles. See Also -------- hdquantiles_sd Examples -------- >>> import numpy as np >>> from scipy.stats.mstats import hdquantiles >>> >>> # Sample data >>> data = np.array([1.2, 2.5, 3.7, 4.0, 5.1, 6.3, 7.0, 8.2, 9.4]) >>> >>> # Probabilities at which to compute quantiles >>> probabilities = [0.25, 0.5, 0.75] >>> >>> # Compute Harrell-Davis quantile estimates >>> quantile_estimates = hdquantiles(data, prob=probabilities) >>> >>> # Display the quantile estimates >>> for i, quantile in enumerate(probabilities): ... print(f"{int(quantile * 100)}th percentile: {quantile_estimates[i]}") 25th percentile: 3.1505820231763066 # may vary 50th percentile: 5.194344084883956 75th percentile: 7.430626414674935 cNtjtj|t }|j}tjdt|ft}|dkrtj |_ |r|S|dStj |dzt|z }tj}t!|D]r\}} |||dz| z|dzd| z z} | dd| ddz } tj| |} | |d|f<tj| || z dz|d|f<s|d|d|dkf<|d|d|dkf<|r"tj x|d|dkf<|d|dkf<|S|dS)zGComputes the HD quantiles for a 1D array. Returns nan for invalid data.r rN)npsqueezesort compressedviewrsizeemptylenr nanflatarangefloatrcdf enumeratedot) dataprobvarxsortednhdvbetacdfip_wwhd_means Z/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/scipy/stats/_mstats_extras.py_hd_1Dzhdquantiles.._hd_1DPs*RWT__%6%6%;%;G%D%DEEFF L XqTmW - - q55fBG  a5L IacNNU1XX %(t__ 6 6EQqQqS!GacAaC[11B122CRC AfQ((GBqsGfQ1 455BqsGG"1:1dai<"2;1dai<  24& 8Bq$!)| r!TQY,/I!u FcopydtypeNrrDArray 'data' must be at most two dimensional, but got data.ndim = %dr<) maarrayr r atleast_1dasarrayndim ValueErrorapply_along_axis fix_invalid)r+r,axisr-r9r4results r8rrsh< 8DuG 4 4 4D bj&&''A $)q..a%% 9q==68< BCC C$VT4C@@ >&u - - --r:rcRt|dg||}|S)a9 Returns the Harrell-Davis estimate of the median along the given axis. Parameters ---------- data : ndarray Data array. axis : int, optional Axis along which to compute the quantiles. If None, use a flattened array. var : bool, optional Whether to return the variance of the estimate. Returns ------- hdmedian : MaskedArray The median values. If ``var=True``, the variance is returned inside the masked array. E.g. for a 1-D array the shape change from (1,) to (2,). r)rHr-)rr)r+rHr-rIs r8rr|s,,se$C 8 8 8F >>  r:cld}tj|dt}tjtj|}| |||}n9|jdkrtd|jztj||||}tj |d S)a The standard error of the Harrell-Davis quantile estimates by jackknife. Parameters ---------- data : array_like Data array. prob : sequence, optional Sequence of quantiles to compute. axis : int, optional Axis along which to compute the quantiles. If None, use a flattened array. Returns ------- hdquantiles_sd : MaskedArray Standard error of the Harrell-Davis quantile estimates. See Also -------- hdquantiles c $tj|}t|}tjt|t }|dkrtj|_tj|t|dz z }tj }t|D]\}}||||z|d|z z} | dd| ddz } tj |} tj| |ddz| dd<| ddxxtj| ddd|dddzdddz cc<tj| |dz z||<|S)z%Computes the std error for 1D arrays.rrNrr )rrrr#r"r r$r%r&r'rr(r) zeros_likecumsumsqrtr-) r+r,r.r/hdsdvvr2r3r4r5r6mx_s r8_hdsd_1Dz hdquantiles_sd.._hdsd_1Dsl'$//++,, LLxD 7++ q55DI Yq\\E!A#JJ &(t__ 3 3EQqQqS!QqS'**B122CRC A-((CiGCRCL 011CG HHH !DDbD'GEQrEN":;;DDbDA AHHHgcggii1q5122DGG r:Fr;Nrr>r?) r@rAr rrBrCrDrErFrGravel)r+r,rHrSr4rIs r8rrs02 8DuG 4 4 4D bj&&''A $"" 9q==68< BCC C$XtT1== >&u - - - 3 3 5 55r:皙?rVTT皙?cbtj|d}tj||||}||}tj||||}||dz }tjd|dz z |} tj|| |zz || |zzfS)a Selected confidence interval of the trimmed mean along the given axis. Parameters ---------- data : array_like Input data. limits : {None, tuple}, optional None or a two item tuple. Tuple of the percentages to cut on each side of the array, with respect to the number of unmasked data, as floats between 0. and 1. If ``n`` is the number of unmasked data before trimming, then (``n * limits[0]``)th smallest data and (``n * limits[1]``)th largest data are masked. The total number of unmasked data after trimming is ``n * (1. - sum(limits))``. The value of one limit can be set to None to indicate an open interval. Defaults to (0.2, 0.2). inclusive : (2,) tuple of boolean, optional If relative==False, tuple indicating whether values exactly equal to the absolute limits are allowed. If relative==True, tuple indicating whether the number of data being masked on each side should be rounded (True) or truncated (False). Defaults to (True, True). alpha : float, optional Confidence level of the intervals. Defaults to 0.05. axis : int, optional Axis along which to cut. If None, uses a flattened version of `data`. Defaults to None. Returns ------- trimmed_mean_ci : (2,) ndarray The lower and upper confidence intervals of the trimmed data. Fr?)limits inclusiverHr@) r@rAmstatstrimrmean trimmed_stdecountrppfr) r+rZr[alpharHtrimmedtmeantstdedftppfs r8r r sT 8Du % % %Dl4)$OOOG LL  E  FYD Q Q QE t  q B 558B  D 8UT%Z'tEz)9: ; ;;r:cd}tj|d}|jdkrtd|jzt jt j|}| |||Stj||||S)a Returns the Maritz-Jarrett estimators of the standard error of selected experimental quantiles of the data. Parameters ---------- data : ndarray Data array. prob : sequence, optional Sequence of quantiles to compute. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. ctj|}|j}tj||zdzt }tj}tj t|t}tj d|dzt|z }|d|z z }t|D]v\}} ||| dz || z ||| dz || z z } tj| |} tj| |dz} tj| | dzz ||<w|S)Nrr)r=g?r)rrrr!rAastypeintrr(r"r#r r&r)r*rO) r+r4r/r,r2mjxyr3mWC1C2s r8_mjci_1Dzmjci.._mjci_1Ds%wt(()) I a#%--c22( Xc$ii ) ) Ia!7 + + +a / 1Ht__ ( (EQq!A#ac""WWQqs1Q3%7%77A$B$'""BGBQJ''BqEE r:Fr?rr>)r@rArDrErrBrCrF)r+r,rHrtr4s r8rrs  8Du % % %D y1}}248I>?? ? bj&&''A xa   "8T4;;;r:ct|d|z }tjd|dz z }tj||dd|}t |||}|||zz |||zzfS)a Computes the alpha confidence interval for the selected quantiles of the data, with Maritz-Jarrett estimators. Parameters ---------- data : ndarray Data array. prob : sequence, optional Sequence of quantiles to compute. alpha : float, optional Confidence level of the intervals. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. Returns ------- ci_lower : ndarray The lower boundaries of the confidence interval. Of the same length as `prob`. ci_upper : ndarray The upper boundaries of the confidence interval. Of the same length as `prob`. rr\r )alphapbetaprHrH)minrrbr] mquantilesr)r+r,rcrHzxqsmjs r8r r 5sx6 q5y ! !E U2XA  4aqt D D DB tT % % %C SL"q3w, ''r:cd}tj|d}| |||}n9|jdkrtd|jztj||||}|S)aA Computes the alpha-level confidence interval for the median of the data. Uses the Hettmasperger-Sheather method. Parameters ---------- data : array_like Input data. Masked values are discarded. The input should be 1D only, or `axis` should be set to None. alpha : float, optional Confidence level of the intervals. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. Returns ------- median_cihs Alpha level confidence interval. ctj|}t|}t |d|z }t t j|dz |d}t j||z |dt j|dz |dz }|d|z kr8|dz}t j||z |dt j|dz |dz }t j||z dz |dt j||dz }|dz |z||z z }||z |zt||d|zz |zzz }|||zd|z ||dz zz||||z dz zd|z |||z zzf}|S)Nrr\rr) rrrr#ryrlr_ppfr(r') r+rcr/kgkgkkIlambdlimss r8_cihs_1Dzmedian_cihs.._cihs_1Dnswt(()) IIE1U7##  58Q,, - - Yqs1S ! !EIac!C$8$8 8 %<< FA1Q3q%% !A#a(<(<)r@rArDrErF)r+rcrHrrIs r8rrWs. 8Du % % %D $&& 9q==68< BCC C$XtT5AA Mr:cJtj||tj||}}tj||tj||}}t j||z tj|dz|dzzz }dtj|z S)a" Compares the medians from two independent groups along the given axis. The comparison is performed using the McKean-Schrader estimate of the standard error of the medians. Parameters ---------- group_1 : array_like First dataset. Has to be of size >=7. group_2 : array_like Second dataset. Has to be of size >=7. axis : int, optional Axis along which the medians are estimated. If None, the arrays are flattened. If `axis` is not None, then `group_1` and `group_2` should have the same shape. Returns ------- compare_medians_ms : {float, ndarray} If `axis` is None, then returns a float, otherwise returns a 1-D ndarray of floats with a length equal to the length of `group_1` along `axis`. Examples -------- >>> from scipy import stats >>> a = [1, 2, 3, 4, 5, 6, 7] >>> b = [8, 9, 10, 11, 12, 13, 14] >>> stats.mstats.compare_medians_ms(a, b, axis=None) 1.0693225866553746e-05 The function is vectorized to compute along a given axis. >>> import numpy as np >>> rng = np.random.default_rng() >>> x = rng.random(size=(3, 7)) >>> y = rng.random(size=(3, 8)) >>> stats.mstats.compare_medians_ms(x, y, axis=1) array([0.36908985, 0.36092538, 0.2765313 ]) References ---------- .. [1] McKean, Joseph W., and Ronald M. Schrader. "A comparison of methods for studentizing the sample median." Communications in Statistics-Simulation and Computation 13.6 (1984): 751-773. rxrr) r@medianr] stde_medianrabsrOrr()group_1group_2rHmed_1med_2std_1std_2rqs r8rrsdiT222BIg44P4P4PEU(t<<<(t<<< U uu}q5!8(; < <._idfs OO   FF q55F26? "qte|A&&1 FFsAacFlQqtV# EsAaDj1QqsV8#Szr:rx)r@rr rrF)r+rHrs r8rrs],    74d # # # ( ( 5 5D tDzz"4t444r:ctj|d}||}n&tjtj|}|jdkrt d|}t|d}d|d|d z z|d zz }|dddf|dddf|zk d }|dddf|dddf|z k d }||z d |z|zz S) a Evaluates Rosenblatt's shifted histogram estimators for each data point. Rosenblatt's estimator is a centered finite-difference approximation to the derivative of the empirical cumulative distribution function. Parameters ---------- data : sequence Input data, should be 1-D. Masked values are ignored. points : sequence or None, optional Sequence of points where to evaluate Rosenblatt shifted histogram. If None, use the data. Fr?Nrz#The input array should be 1D only !rxg333333?rr rVr\) r@rArrBrCrDAttributeErrorrarsum)r+pointsr/rrnhinlos r8r r s 8Du % % %D ~rz&1122 yA~~BCCC AT%%%A quQqTzQY&A $<6$qqq&>A- - 2 21 5 5C $<&aaa.1, , 1 1! 4 4C G1Q r:)rNF)rF)rN)rUrWrXN)rrXN)rXN)N)__doc____all__numpyrr rnumpy.mar@rrr]scipy.stats.distributionsrrrrrrrr rr rrrr r:r8rs   """""""" %%%%%%::::::::::::].].].].@4<6<6<6<6~7B%)0<0<0<0