(ph?Sr/SQrSSKrSSKJrJr SSKJr SSKJr SSK J r SSK J r JrJrJr SS jrSS jrSS jrSS jrSS jrSSjrSSjrSSjrSSjrSSjrg)zB Additional statistics functions with support for masked arrays. ) compare_medians_ms hdquantileshdmedianhdquantiles_sd idealfourths median_cihsmjcimquantiles_cimjrshtrimmed_mean_ciN)float64ndarray) MaskedArray) _mstats_basic)normbetatbinomctSn[R"US[S9n[R"[R "U55nUbUR S:Xa U"XU5nO@UR S:a[SUR -5e[R"XBXU5n[R"USS9$)at Computes quantile estimates with the Harrell-Davis method. The quantile estimates are calculated as a weighted linear combination of order statistics. Parameters ---------- data : array_like Data array. prob : sequence, optional Sequence of probabilities at which to compute the quantiles. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. var : bool, optional Whether to return the variance of the estimate. Returns ------- hdquantiles : MaskedArray A (p,) array of quantiles (if `var` is False), or a (2,p) array of quantiles and variances (if `var` is True), where ``p`` is the number of quantiles. See Also -------- hdquantiles_sd Examples -------- >>> import numpy as np >>> from scipy.stats.mstats import hdquantiles >>> >>> # Sample data >>> data = np.array([1.2, 2.5, 3.7, 4.0, 5.1, 6.3, 7.0, 8.2, 9.4]) >>> >>> # Probabilities at which to compute quantiles >>> probabilities = [0.25, 0.5, 0.75] >>> >>> # Compute Harrell-Davis quantile estimates >>> quantile_estimates = hdquantiles(data, prob=probabilities) >>> >>> # Display the quantile estimates >>> for i, quantile in enumerate(probabilities): ... print(f"{int(quantile * 100)}th percentile: {quantile_estimates[i]}") 25th percentile: 3.1505820231763066 # may vary 50th percentile: 5.194344084883956 75th percentile: 7.430626414674935 c4[R"[R"UR5R [ 555nUR n[R"S[U54[5nUS:a#[RUl U(aU$US$[R"US-5[U5- n[Rn[!U5HeupU"XdS-U -US-SU - -5n U SSU SS- n [R""X5n XSU4'[R""XU - S-5USU4'Mg USUSUS:H4'USUSUS:H4'U(a$[R=USUS:H4'USUS:H4'U$US$)zGComputes the HD quantiles for a 1D array. Returns nan for invalid data.r rN)npsqueezesort compressedviewrsizeemptylenr nanflatarangefloatrcdf enumeratedot) dataprobvarxsortednhdvbetacdfip_wwhd_means M/var/www/html/venv/lib/python3.13/site-packages/scipy/stats/_mstats_extras.py_hd_1Dhdquantiles.._hd_1DPsw**RWWT__%6%;%;G%DEF LL XXqTmW - q5ffBG a5L IIacNU1X %((t_EQqS!GacAaC[1B12CR AffQ(GqsGffQ1 45BqsG %#1:1dai<"2;1dai< 24&& 8Bq$!)| r!TQY,/I!u FcopydtyperrDArray 'data' must be at most two dimensional, but got data.ndim = %dr;) maarrayr r atleast_1dasarrayndim ValueErrorapply_along_axis fix_invalid)r)r*axisr+r7r2results r6rrsh< 88DuG 4D bjj&'A $))q.% 99q=68< BC C$$V4C@ >>&u --r9c:[US/XS9nUR5$)a Returns the Harrell-Davis estimate of the median along the given axis. Parameters ---------- data : ndarray Data array. axis : int, optional Axis along which to compute the quantiles. If None, use a flattened array. var : bool, optional Whether to return the variance of the estimate. Returns ------- hdmedian : MaskedArray The median values. If ``var=True``, the variance is returned inside the masked array. E.g. for a 1-D array the shape change from (1,) to (2,). ?)rGr+)rr)r)rGr+rHs r6rr|s!,se$ 8F >> r9clSn[R"US[S9n[R"[R "U55nUc U"X5nO?UR S:a[SUR -5e[R"X2X5n[R"USS9R5$)a The standard error of the Harrell-Davis quantile estimates by jackknife. Parameters ---------- data : array_like Data array. prob : sequence, optional Sequence of quantiles to compute. axis : int, optional Axis along which to compute the quantiles. If None, use a flattened array. Returns ------- hdquantiles_sd : MaskedArray Standard error of the Harrell-Davis quantile estimates. See Also -------- hdquantiles c [R"UR55n[U5n[R"[U5[ 5nUS:a[R Ul[R"U5[US- 5- n[Rn[U5HupxU"XSU-USU- -5n U SSU SS- n [R"U5n [R"XSS-5U SS&U SS===[R"U SSS2USSS2-5SSS2- sss&[R"U R!5US- -5XG'M U$)z%Computes the std error for 1D arrays.rrNrr )rrrr!r r r"r#r$r%rr&r' zeros_likecumsumsqrtr+) r)r*r,r-hdsdvvr0r1r2r3r4mx_s r6_hdsd_1D hdquantiles_sd.._hdsd_1Ds3''$//+, LxxD 7+ q5DI YYq\E!A#J &((t_EQqS!QqS'*B12CR A--(CiiCRL 01CG H !DbD'GEQrEN":;DbDA AHggcggi1q512DG% r9Fr:rr=r>) r?r@r rrArBrCrDrErFravel)r)r*rGrSr2rHs r6rrs02 88DuG 4D bjj&'A $" 99q=68< BC C$$XT= >>&u - 3 3 55r9cH[R"USS9n[R"XX$S9nUR U5n[R "XX$S9nUR U5S- n[R"SUS- - U5n [R"XiU-- XiU--45$)a3 Selected confidence interval of the trimmed mean along the given axis. Parameters ---------- data : array_like Input data. limits : {None, tuple}, optional None or a two item tuple. Tuple of the percentages to cut on each side of the array, with respect to the number of unmasked data, as floats between 0. and 1. If ``n`` is the number of unmasked data before trimming, then (``n * limits[0]``)th smallest data and (``n * limits[1]``)th largest data are masked. The total number of unmasked data after trimming is ``n * (1. - sum(limits))``. The value of one limit can be set to None to indicate an open interval. Defaults to (0.2, 0.2). inclusive : (2,) tuple of boolean, optional If relative==False, tuple indicating whether values exactly equal to the absolute limits are allowed. If relative==True, tuple indicating whether the number of data being masked on each side should be rounded (True) or truncated (False). Defaults to (True, True). alpha : float, optional Confidence level of the intervals. Defaults to 0.05. axis : int, optional Axis along which to cut. If None, uses a flattened version of `data`. Defaults to None. Returns ------- trimmed_mean_ci : (2,) ndarray The lower and upper confidence intervals of the trimmed data. Fr>)limits inclusiverGr@) r?r@mstatstrimrmean trimmed_stdecountrppfr) r)rWrXalpharGtrimmedtmeantstdedftppfs r6r r sT 88Du %Dll4)OG LL E   Y QE t q B 5558B D 88U%Z'Ez)9: ;;r9cSn[R"USS9nURS:a[SUR-5e[R "[R "U55nUcU"X5$[R"X2X5$)aT Returns the Maritz-Jarrett estimators of the standard error of selected experimental quantiles of the data. Parameters ---------- data : ndarray Data array. prob : sequence, optional Sequence of quantiles to compute. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. cv[R"UR55nURn[R"U5U-S-R [ 5n[Rn[R"[U5[5n[R"SUS-[S9U- nUSU- - n[U5HnupU"XiS- X)- 5U"XyS- X)- 5- n [R"X5n [R"XS-5n [R"XS-- 5XX'Mp U$)NrJr)r<g?r)rrrrr@astypeintrr&r r!r r$r'r(rO) r)r2r-r*r0mjxyr1mWC1C2s r6_mjci_1Dmjci.._mjci_1Dswwt() II a#%--c2(( XXc$i ) IIa!7 +a / 1Ht_EQA#ac"WQs13%77AB'"BGGBQJ'BE %  r9Fr>rr=)r?r@rCrDrrArBrE)r)r*rGrqr2s r6rrs~  88Du %D yy1}248II>? ? bjj&'A   ""84;;r9c[USU- 5n[R"SUS- - 5n[R"XSSUS9n[ XUS9nXTU-- XTU--4$)a} Computes the alpha confidence interval for the selected quantiles of the data, with Maritz-Jarrett estimators. Parameters ---------- data : ndarray Data array. prob : sequence, optional Sequence of quantiles to compute. alpha : float, optional Confidence level of the intervals. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. Returns ------- ci_lower : ndarray The lower boundaries of the confidence interval. Of the same length as `prob`. ci_upper : ndarray The upper boundaries of the confidence interval. Of the same length as `prob`. rrYr )alphapbetaprGrG)minrr_rZ mquantilesr)r)r*r`rGzxqsmjs r6r r 5sc6 q5y !E U2XA   4aqt DB t %C SL"3w, ''r9cSn[R"USS9nUc U"X5nU$URS:a[SUR-5e[R"X2X5nU$)a Computes the alpha-level confidence interval for the median of the data. Uses the Hettmasperger-Sheather method. Parameters ---------- data : array_like Input data. Masked values are discarded. The input should be 1D only, or `axis` should be set to None. alpha : float, optional Confidence level of the intervals. axis : int or None, optional Axis along which to compute the quantiles. If None, use a flattened array. Returns ------- median_cihs Alpha level confidence interval. c[R"UR55n[U5n[ USU- 5n[ [ R"US- US55n[ R"X#- US5[ R"US- US5- nUSU- :a;US-n[ R"X#- US5[ R"US- US5- n[ R"X#- S- US5[ R"X2S5- nUS- U-XE- - nX#- U-[X2SU-- U--5- nXpU-SU- XS- --XpX#- S- -SU- XU- --4nU$)NrrYrJr) rrrr!rwrir_ppfr&r%) r)r`r-kgkgkkIlambdlimss r6_cihs_1Dmedian_cihs.._cihs_1Dns_wwt() IE1U7#  58Q, - YYqs1S !EIIac!C$8 8 %< FA13q% !A#a(<rr=)r?r@rCrDrE)r)r`rGrrHs r6rrWst. 88Du %D $& M 99q=68< BC C$$XTA Mr9c@[R"XS9[R"XS9pC[R"XS9[R"XS9pe[R "X4- 5[R "US-US--5- nS[R"U5- $)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. rvrr) r?medianrZ stde_medianrabsrOrr&)group_1group_2rGmed_1med_2std_1std_2rns r6rrs|dii2BIIg4PE((<((<  u}q5!8(; <._idfs OO  F q5FF266? "qte|A& FsAcFlQtV# EsADj1qsV8#zr9rv)r?rrrrE)r)rGrs r6rrsD,  774 # ( ( 5D Dz""4t44r9c[R"USS9nUcUnO*[R"[R"U55nUR S:wa [ S5eUR5n[USS9nSUSUS - -US -- nUSS2S4USSS24U-:*RS 5nUSS2S4USSS24U- :RS 5nXV- S U-U-- $) 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 !rvg333333?rr 皙?rY) r?r@rrArBrCAttributeErrorr^rsum)r)pointsr-rrnhinlos r6r r s 88Du %D ~rzz&12 yyA~BCC AT%A quQqTzQY&A $<6$q&>A- - 2 21 5C $<&a.1, , 1 1! 4C G1Q r9)g?rJg?NF)rF)rN))rr)TT皙?N)rrN)rN)N)__doc____all__numpyrr rnumpy.mar?rrrZscipy.stats.distributionsrrrrrrrr rr rrrr r9r6rsl " %::].@4<6~7B%)0