U |e< @sdZddddddddd d g Zd d lZd d lmZmZmZd d lmZd dlm Z ddl m Z d dl mZmZmZmZedddgd dfddZd$ddZedddgd fddZd%dd Zdddgd fddZdddgdd fddZd&d dZd'd!dZd(d"dZd)d#d Zd S)*zB Additional statistics functions with support for masked arrays. compare_medians_ms hdquantileshdmedianhdquantiles_sd idealfourths median_cihsmjcimquantiles_cimjrshtrimmed_mean_ciN)float_int_ndarray) MaskedArray) _mstats_basic)normbetatbinomg??g?FcCsdd}tj|dtd}tj|ddd}|dks:|jdkrH||||}n*|jdkr`td |jt|||||}tj|dd S) 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 quantiles to compute. 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 c SsJtt|t}|j}tdt|ft }|dkrTtj |_ |rL|S|dSt |dt |}tj}t|D]t\}} |||d| |dd| } | dd| dd} t| |} | |d|f<t| || d|d|f<qx|d|d|dkf<|d|d|dkf<|rBtj |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) dataprobvarxsortednZhdvbetacdfip_wwZhd_meanr3W/var/www/website-v5/atlas_env/lib/python3.8/site-packages/scipy/stats/_mstats_extras.py_hd_1D;s,   "zhdquantiles.._hd_1DFcopydtyperr7ndminNrDArray 'data' must be at most two dimensional, but got data.ndim = %dr7)maarrayr rndim ValueErrorapply_along_axis fix_invalid)r(r)axisr*r5r0resultr3r3r4rs rcCst|dg||d}|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)rCr*)rr)r(rCr*rDr3r3r4rgscCsvdd}tj|dtd}tj|ddd}|dkr<|||}n(|jdkrTtd |jt||||}tj|dd 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 Sst|}t|}tt|t}|dkr6tj|_t|t |d}t j }t |D]\}}|||||d|} | dd| dd} t |} t| |dd| dd<| ddt| ddd|dddddd7<t| |d||<qZ|S)z%Computes the std error for 1D arrays.rrNrr )rrrr rr r!r"r#r$rr%r& zeros_likecumsumsqrtr*) r(r)r+r,Zhdsdvvr.r/r0r1r2Zmx_r3r3r4_hdsd_1Ds <z hdquantiles_sd.._hdsd_1DFr6rr9Nrr;r<) r=r>r rr?r@rArBravel)r(r)rCrIr0rDr3r3r4rs  皙?rLTT皙?c Cs|tj|dd}tj||||d}||}tj||||d}||d}td|d|} t || ||| |fS)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 inclusiverCr@) r=r>mstatstrimrmean trimmed_stdecountrppfr) r(rOrPalpharCtrimmedtmeanZtstdedfZtppfr3r3r4r s* cCsddd}tj|dd}|jdkr.td|jtj|ddd}|d krP|||St||||Sd 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. c Sst|}|j}t||dt}tj}t t |t }tj d|dt d|}|d|}t |D]b\}} ||| d|| ||| d|| } t| |} t| |d} t| | d||<qn|S)Nrr)r8g?r)rrrrr>astyper rr%rr r r#r&r'rG) r(r0r,r)r.Zmjxyr/mWC1C2r3r3r4_mjci_1Ds ( zmjci.._mjci_1DFr<rr;rr9N)r=r>r?r@rrA)r(r)rCrcr0r3r3r4rs  cCsZt|d|}td|d}tj||dd|d}t|||d}||||||fS)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`. rrQr )alphapbetaprCrC)minrrWrR mquantilesr)r(r)rXrCzZxqZsmjr3r3r4r s cCsVdd}tj|dd}|dkr*|||}n(|jdkrBtd|jt||||}|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. c Ss>t|}t|}t|d|}tt|d|d}t|||dt|d|d}|d|kr|d8}t|||dt|d|d}t||d|dt||d}|d|||}|||t ||d||}|||d|||d||||dd||||f}|S)NrrQrr) rrrr rgintr_ppfr%r$) r(rXr,kgkZgkkIlambdZlimsr3r3r4_cihs_1DYs$ $$$&zmedian_cihs.._cihs_1DFr<Nrr;)r=r>r?r@rA)r(rXrCrprDr3r3r4rBs  cCsntj||dtj||d}}tj||dtj||d}}t||t|d|d}dt|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. rfrr) r=medianrR stde_medianrabsrGrr%)Zgroup_1Zgroup_2rCZmed_1Zmed_2Zstd_1Zstd_2r`r3r3r4rus 2  $cCs>dd}tj||dt}|dkr,||St|||SdS)aC Returns an estimate of the lower and upper quartiles. Uses the ideal fourths algorithm. Parameters ---------- data : array_like Input array. axis : int, optional Axis along which the quartiles are estimated. If None, the arrays are flattened. Returns ------- idealfourths : {list of floats, masked array} Returns the two internal values that divide `data` into four parts using the ideal fourths algorithm either along the flattened array (if `axis` is None) or along `axis` of `data`. cSs|}t|}|dkr$tjtjgSt|ddd\}}t|}d|||d|||}||}d||||||d}||gS)Ng@g?r)rr rr!divmodrj)r(r]r,jhZqlorlZqupr3r3r4_idfs   zidealfourths.._idfrfN)r=rrrrA)r(rCrxr3r3r4rs  cCstj|dd}|dkr|}ntj|ddd}|jdkr>td|}t|dd}d|d |d |d }|dddf|dddf|kd }|dddf|dddf|kd }||d ||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<Nrr9z#The input array should be 1D only !rfg333333?rr rLrQ)r=r>rr?AttributeErrorrVrsum)r(pointsr,rrwZnhiZnlor3r3r4r s  **)rF)rKrMrNN)rNN)N)N)N)__doc____all__numpyrr r rnumpy.mar=rrrRZscipy.stats.distributionsrrrrlistrrrr rrrrrr r3r3r3r4s<   K ? 3-" 3 9 (