o Eb9@sdZgdZddlZddlmZmZmZddlmZddlm Z ddl m Z ddl mZmZmZmZegd dd fd d Zd#ddZegd dfddZ  d$ddZgd dfddZgd ddfddZd%ddZd&ddZd&dd Zd&d!d"ZdS)'zB Additional statistics functions with support for masked arrays. ) compare_medians_ms hdquantileshdmedianhdquantiles_sd idealfourths median_cihsmjcimquantiles_cimjrshtrimmed_mean_ciN)float_int_ndarray) MaskedArray) _mstats_basic)normbetatbinom)g??g?FcCsdd}tj|dtd}tj|ddd}|dus|jdkr$||||}n|jdkr0td |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 SsHtt|t}|j}tdt|ft }|dkr*tj |_ |r&|S|dSt |dt |}tj}t|D]:\}} |||d| |dd| } | dd| dd} t| |} | |d|f<t| || d|d|f<q<|d|d|dkf<|d|d|dkf<|rtj |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_meanr3._hd_1DFcopydtyperr7ZndminNrDArray 'data' must be at most two dimensional, but got data.ndim = %dr7)maarrayr rndim ValueErrorapply_along_axis fix_invalid)r(r)axisr*r5r0resultr3r3r4rs rrcCst|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)rBr*)rr)r(rBr*rCr3r3r4rgsrcCsvdd}tj|dtd}tj|ddd}|dur|||}n|jdkr*td |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 st|t}tt|t}|dkrtj|_t|t |d}t j }t |D]>\}}|||d||dd|}|dd|ddtj fddt|Dtd} t| |d||<q-|S)z%Computes the std error for 1D arrays.rrNrcs@g|]}d|d||d|ddqS)Nrr3).0kr2r+r3r4 s8z4hdquantiles_sd.._hdsd_1D..r8)rrrr rr r!r"r#r$rr%r&Zfromiterrangesqrtr*) r(r)r,ZhdsdZvvr.r/r0r1Zmx_r3rFr4_hdsd_1Ds" z hdquantiles_sd.._hdsd_1DFr6rr9Nrr:r;) r<r=r rr>r?r@rAZravel)r(r)rBrKr0rCr3r3r4rs  r皙?rMTT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 inclusiverBr@) r<r=mstatsZtrimrZmeanZ trimmed_stdecountrppfr) r(rPrQalpharBZtrimmedZtmeanZtstdeZdfZtppfr3r3r4r s* r cCs`dd}tj|dd}|jdkrtd|jtj|ddd}|d ur(|||St||||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]1\}} ||| d|| ||| d|| } t| |} t| |d} t| | d||<q7|S)NrrrHg?r)rrrrr=Zastyper rr%rr r r#r&r'rJ) r(r0r,r)r.Zmjxyr/mWZC1ZC2r3r3r4_mjci_1Ds ( zmjci.._mjci_1DFr;rr:rr9N)r<r=r>r?rr@)r(r)rBr[r0r3r3r4rs  rcCsZt|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`. rrRr )ZalphapZbetaprBrB)minrrUrSZ mquantilesr)r(r)rVrBzZxqZsmjr3r3r4rs rcCsXdd}tj|dd}|dur|||}|S|jdkr"td|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|krK|d8}t|||dt|d|d}t||d|dt||d}|d|||}|||t ||d||}|||d|||d||||dd||||f}|S)NrrRrr) rrrr r]intrZ_ppfr%r$) r(rVr,rEZgkZgkkIZlambdZlimsr3r3r4_cihs_1DWs$ $$$&zmedian_cihs.._cihs_1DFr;Nrr:)r<r=r>r?r@)r(rVrBrarCr3r3r4r@s  rcCsntj||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`. r\rr) r<ZmedianrSZ stde_medianrabsrJrr%)Zgroup_1Zgroup_2rBZmed_1Zmed_2Zstd_1Zstd_2rZr3r3r4rss   $rcCs:dd}tj||dt}|dur||St|||S)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|}|dkrtjtjgSt|ddd\}}t|}d|||d|||}||}d||||||d}||gS)Ng@g?r)rr rr!divmodr_)r(rWr,jhZqlorEZqupr3r3r4_idfs   zidealfourths.._idfr\N)r<rrrr@)r(rBrgr3r3r4rs  rcCstj|dd}|dur|}ntj|ddd}|jdkrtd|}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 !r\g333333?rr rMrR)r<r=rr>AttributeErrorrTrsum)r(Zpointsr,rrfZnhiZnlor3r3r4r s  **r )rF)rLrNrON)rON)N)__doc____all__Znumpyrr r rZnumpy.mar<rrrSZscipy.stats.distributionsrrrrlistrrrr rrrrrr r3r3r3r4s(    K= 3- " 3 !(