+ 0i?Rt.ROt^RIt^RIHtHt^RIHt^RIHt^RI H t ^RI H t HtHtHtRRltRRltRRltRR ltRR ltRR ltRR ltRR ltRRltRRltR#)zB Additional statistics functions with support for masked arrays. N)float64ndarray) MaskedArray) _mstats_basic)normbetatbinomcRp\P!VR\R7p\P!\P !V44pVeVP ^8Xd V!WV4pMAVP ^8d\RVP 24h\P!WBWV4p\P!VRR7#)at 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 c\P!\P!VP4P \ 444pVP p\P!^\V43\4pV^8d)\PVn V'dV#V^,#\P!V^,4\V4, p\Pp\!V4FwrV!Wd^,V ,V^,^V , ,4p V R,V RR, p \P"!W4p W^V3&\P"!WV , ^,4V^V3&K V^,V^V^8H3&VR,V^V^8H3&V'd%\P;V^V^8H3&V^V^8H3&V#V^,#)zGComputes the HD quantiles for a 1D array. Returns nan for invalid data.NNN)npsqueezesort compressedviewrsizeemptylenrnanflatarangefloatrcdf enumeratedot) dataprobvarxsortednhdvbetacdfip_wwhd_means &&& X/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/stats/_mstats_extras.py_hd_1Dhdquantiles.._hd_1DPsu**RWWT__%6%;%;G%DEF LL XXqTmW - q5ffBG a5L IIacNU1X %((t_EQqS!GacAaC[1B2CR AffQ(GqsGffQ1 45BqsG %#1:1dai<"2;1dai< 24&& 8Bq$!)| r!TQY,/I!u FcopydtypeBArray 'data' must be at most two dimensional, but got data.ndim = r0) maarrayrr atleast_1dasarrayndim ValueErrorapply_along_axis fix_invalid)rraxisr r,r'results&&&& r+ hdquantilesr>sh< 88DuG 4D bjj&'A $))q.% 99q= 448II;@A A$$V4C@ >>&u --r.c@\VR.WR7pVP4#)a Returns the Harrell-Davis estimate of the median along the given axis. Parameters ---------- data : ndarray Data array. axis : int, optional Axis along which to compute the quantiles. If None, use a flattened array. var : bool, optional Whether to return the variance of the estimate. Returns ------- hdmedian : MaskedArray The median values. If ``var=True``, the variance is returned inside the masked array. E.g. for a 1-D array the shape change from (1,) to (2,). ?)r<r )r>r)rr<r r=s&&& r+hdmedianrA|s!,se$ 8F >> r.c|Rp\P!VR\R7p\P!\P !V44pVf V!W4pM@VP ^8d\RVP 24h\P!W2W4p\P!VRR7P4#)a The standard error of the Harrell-Davis quantile estimates by jackknife. Parameters ---------- data : array_like Data array. prob : sequence, optional Sequence of quantiles to compute. axis : int, optional Axis along which to compute the quantiles. If None, use a flattened array. Returns ------- hdquantiles_sd : MaskedArray Standard error of the Harrell-Davis quantile estimates. See Also -------- hdquantiles c V\P!VP44p\V4p\P!\V4\ 4pV^8d\P Vn\P!V4\V^, 4, p\Pp\V4FwrxV!WSV,V^V, ,4p V R,V RR, p \P!V4p \P!WRR,4V R&V RR;;;\P!V RRR1,VR^R1,,4RRR1,, uuu%\P!V P!4V^, ,4WG&K V#)z%Computes the std error for 1D arrays.r Nr)rrrrrrrrrrrrr zeros_likecumsumsqrtr ) rrr!r"hdsdvvr%r&r'r(r)mx_s && r+_hdsd_1D hdquantiles_sd.._hdsd_1Ds/''$//+, LxxD 7+ q5DI YYq\E!A#J &((t_EQqS!QqS'*B2CR A--(CiiCRL 01CG H !DbD'GEQrEN":;DbDA AHggcggi1q512DG% r.Fr/r2r3) r4r5rrr6r7r8r9r:r;ravel)rrr<rJr'r=s&&& r+hdquantiles_sdrMs02 88DuG 4D bjj&'A $" 99q= 448II;@A A$$XT= >>&u - 3 3 55r.c\P!VRR7p\P!WW$R7pVP V4p\P !WW$R7pVP V4^, p\P!^VR, , V4p \P!WiV,, WiV,,34#)a3 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. Fr3)limits inclusiver<@) r4r5mstatstrimrmean trimmed_stdecountrppfr) rrOrPalphar<trimmedtmeantstdedftppfs &&&&& r+trimmed_mean_cir^sT 88Du %Dll4)OG LL E   Y QE t q B 5558B D 88U%Z'Ez)9: ;;r.c$Rp\P!VRR7pVP^8d\RVP 24h\P !\P !V44pVf V!W4#\P!W2W4#)aT Returns the Maritz-Jarrett estimators of the standard error of selected experimental quantiles of the data. Parameters ---------- data : ndarray Data array. prob : sequence, optional Sequence of quantiles to compute. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. c\P!VP44pVPp\P!V4V,R,P \ 4p\Pp\P!\V4\4p\P!^V^,\R7V, pVRV, , p\V4FwrV!Wi^, W), 4V!Wy^, W), 4, p \P!W4p \P!W^,4p \P!W^,, 4WX&K V#)r@)r1g?)rrrrr5astypeintrrrrrrrrrF) rr'r"rr%mjxyr&mWC1C2s && r+_mjci_1Dmjci.._mjci_1Dswwt() II a#%--c2(( XXc$i ) IIa!7 +a / 1Ht_EQA#ac"WQs13%77AB'"BGGBQJ'BE %  r.Fr3r2)r4r5r8r9rr6r7r:)rrr<rjr's&&& r+mjcirls  88Du %D yy1}004 {<= = bjj&'A   ""84;;r.c\V^V, 4p\P!^VR, , 4p\P!W^^VR7p\ WVR7pWTV,, WTV,,3#)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`. rQ)alphapbetapr<r<)minrrWrR mquantilesrl)rrrXr<zxqsmjs&&&& r+mquantiles_cimjrv5sc6 q5y !E U2XA   4aqt DB t %C SL"3w, ''r.cRp\P!VRR7pVf V!W4pV#VP^8d\RVP 24h\P!W2W4pV#)a 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. c\P!VP44p\V4p\ V^V, 4p\ \ P!VR, VR44p\ P!W#, VR4\ P!V^, VR4, pV^V, 8dLV^,p\ P!W#, VR4\ P!V^, VR4, p\ P!W#, ^, VR4\ P!W2R4, pV^, V,WE, , pW#, V,\W2^V,, V,,4, pWpV,,^V, W^, ,,,WpW#, ^, ,,^V, WV, ,,,3pV#)r rQr@) rrrrrqrbr _ppfrr) rrXr"kgkgkkIlambdlimss && r+_cihs_1Dmedian_cihs.._cihs_1Dns_wwt() IE1U7#  58Q, - YYqs1S !EIIac!C$8 8 %< FA13q% !A#a(<=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. rp) r4medianrR stde_medianrabsrFrr)group_1group_2r<med_1med_2std_1std_2rgs&&& r+compare_medians_msrs|dii2BIIg4PE((<((<  u}q5!8(; <._idfs OO  F q5FF266? "qte|A& FsAcFlQtV# EsADj1qsV8#zr.rp)r4rrrr:)rr<rs&& r+ idealfourthsrsD,  774 # ( ( 5D Dz""4t44r.c<\P!VRR7pVfTpM*\P!\P!V44pVP ^8wd \ R4hVP4p\VRR7pRVR,V^,, ,VR ,, pVR ,VR ,V,8*P^4pVR ,VR ,V, 8P^4pWV, RV,V,, #) 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. Fr3Nz#The input array should be 1D only !rpg333333?rQr皙?)NNNN)Nr) r4r5rr6r7r8AttributeErrorrVrsum)rpointsr"rrnhinlos&& r+rshrs 88Du %D ~rzz&12 yyA~BCC AT%A quQqTzQY&A <6&>A- - 2 21 5C <&.1, , 1 1! 4C G1Q r.) rr>rArMrrrlrvrr^)g?r@g?NF)rF)rN))rr)TT皙?N)rrN)rN)N)__doc____all__numpyrrrnumpy.mar4rrrRscipy.stats.distributionsrrrr r>rArMr^rlrvrrrrr.r+rsc " %::].@4<6~0