a jA@sdZgdZddlZddlmZmZddlmZddlmZddl m Z ddl m Z mZmZmZegd dd fd d Zd#ddZegd dfddZd$ddZgd dfddZgd ddfddZd%ddZd&ddZd'dd Zd(d!d"ZdS))zB Additional statistics functions with support for masked arrays. ) compare_medians_ms hdquantileshdmedianhdquantiles_sd idealfourths median_cihsmjcimquantiles_cimjrshtrimmed_mean_ciN)float64ndarray) MaskedArray) _mstats_basic)normbetatbinom)g??g?FcCsdd}tj|dtd}tt|}|dus:|jdkrH||||}n*|jdkr`td|jt|||||}tj |dd S) a$ 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 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 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 compressedviewr sizeemptylenr nanflatarangefloatrcdf enumeratedot) dataprobvarxsortednZhdvbetacdfip_wwZhd_meanr2@E:\soccer\ml_env\Lib\site-packages\scipy/stats/_mstats_extras.py_hd_1DPs,   "zhdquantiles.._hd_1DFcopydtypeNrrDArray 'data' must be at most two dimensional, but got data.ndim = %dr6) maarrayr r atleast_1dasarrayndim ValueErrorapply_along_axis fix_invalid)r'r(axisr)r4r/resultr2r2r3rs4 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)rCr2r2r3r|srcCsvdd}tj|dtd}tt|}|dur<|||}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 )rrrrrr r r!r"r#rr$r%Z zeros_likeZcumsumsqrtr)) r'r(r*r+Zhdsdvvr-r.r/r0r1Zmx_r2r2r3_hdsd_1Ds <z hdquantiles_sd.._hdsd_1DFr5Nrr8r9) r:r;r rr<r=r>r?r@rAZravel)r'r(rBrFr/rCr2r2r3rs  r皙?rHTT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. Fr9)limits inclusiverBr@) r:r;mstatsZtrimrmeanZ trimmed_stdecountrppfr) r'rKrLalpharBZtrimmedZtmeanZtstdedfZtppfr2r2r3r s* r cCsddd}tj|dd}|jdkr.td|jtt|}|durP|||St||||SdS)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)r7g?r)rrrrr;Zastypeintrr$rrr r"r%r&rD) r'r/r+r(r-Zmjxyr.mWZC1ZC2r2r2r3_mjci_1Ds ( zmjci.._mjci_1DFr9rr8N)r:r;r>r?rr<r=r@)r'r(rBrYr/r2r2r3rs  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`. rrMr )ZalphapZbetaprBrB)minrrQrNZ mquantilesr)r'r(rRrBzxqZsmjr2r2r3r5s rcCsVdd}tj|dd}|dur*|||}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)NrrMrr) rrrrr[rTrZ_ppfr$r#) r'rRr+kZgkZgkkIlambdZlimsr2r2r3_cihs_1Dns$ $$$&zmedian_cihs.._cihs_1DFr9Nrr8)r:r;r>r?r@)r'rRrBrarCr2r2r3rWs  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`. 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. rZrr) r:ZmedianrNZ stde_medianrabsrDrr$)Zgroup_1Zgroup_2rBZmed_1Zmed_2Zstd_1Zstd_2rXr2r2r3rs 2  $rcCs>dd}tj||dt}|dur,||St|||SdS)aC Returns an estimate of the lower and upper quartiles. Uses the ideal fourths algorithm. Parameters ---------- data : array_like Input array. axis : int, optional Axis along which the quartiles are estimated. If None, the arrays are flattened. Returns ------- idealfourths : {list of floats, masked array} Returns the two internal values that divide `data` into four parts using the ideal fourths algorithm either along the flattened array (if `axis` is None) or along `axis` of `data`. cSs|}t|}|dkr$tjtjgSt|ddd\}}t|}d|||d|||}||}d||||||d}||gS)Ng@g?r)rrrr divmodrT)r'rUr+jhZqlor^Zqupr2r2r3_idfs   zidealfourths.._idfrZN)r:rrrr@)r'rBrgr2r2r3rs  rcCstj|dd}|dur|}ntt|}|jdkr>td|}t|dd}d|d|d |d }|dddf|dddf|k d }|dddf|dddf|k d }||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. Fr9Nrz#The input array should be 1D only !rZg333333?rr rHrM) r:r;rr<r=r>AttributeErrorrPrsum)r'Zpointsr+rrfZnhiZnlor2r2r3r s  **r )rF)rGrIrJN)rJN)N)N)N)__doc____all__numpyrr r Znumpy.mar:rrrNZscipy.stats.distributionsrrrrlistrrrr rrrrrr r2r2r2r3s&   ` ? 3-" 3 9 (