!g: dZddlZddlmZddlmZegddddddfd Zd(d Zd)d Z e Z d*d Z d+d Z e dk(rejdZee eejdj#ddZee eeeedeeedeeedej$eZej)eZej.ed<ee ededdfD]Zee eedfe eedfk(j5eeeedfeeedfk(j5eej6j9ej:eedfeeedfdk(j5dD]Zee eee eek(j5eeeeeeek(j5eej6j9ej:eeeeedk(j5eej6jej:ee eddk(j5ej>eefj@Z!dD];Zee e!ede ej@edz k(j5=ejDjGe ejddddejdzdz dz ejDjGe ejddddejdzdz dz ejDjGe ejddejdzdz dz edeeeddgee edddfee edddfe edddfk(j5gd Z$dZ%e%rddl&m'Z(e(jRe(jTd!e(jVe edddfe$d"#edddfd$%e(jVej6jejXedddfe$dejXedddfe$dd$%e(jZe edddfe$d"#edddfd&e(jZej6jejXedddfe$dejXedddfe$dd&e(jRe(jTd'e(jVedddfe edddfe$d"#d$%e(jVejXedddfe$dej6jejXedddfe$dd$%e(jZedddfe edddfe$d"#d&e(jZejXedddfe$dej6jejXedddfe$dd&e(j\yy),aQget versions of mstats percentile functions that also work with non-masked arrays uses dispatch to mstats version for difficult cases: - data is masked array - data requires nan handling (masknan=True) - data should be trimmed (limit is non-empty) handle simple cases directly, which does not require apply_along_axis changes compared to mstats: plotting_positions for n-dim with axis argument addition: plotting_positions_w1d: with weights, 1d ndarray only TODO: consistency with scipy.stats versions not checked docstrings from mstats not updated yet code duplication, better solutions (?) convert examples to tests rename alphap, betap for consistency timing question: one additional argsort versus apply_along_axis weighted plotting_positions - I have not figured out nd version of weighted plotting_positions - add weighted quantiles N)mastats)g?g?g?皙?Fct|tjjr%tj j ||||||S|rJtj j ||||||}tj|tjS|rtj|}|jratj||}tj j ||||||}tj|tjStj|} tj|dd} || d|z |z zz} d} || j} d }n:tj| j|}tj | |} d } tj"| d } | j$d }t'| j$}| ||<|d k(r$tj(t+| t, S|dk(r tj.| | j$S|| z| z}tj0|j3d|dz j5t6}dg| jz}t9d|d <||z j3d d|}d|z | |dz z|| |zz}| rtj |d |dzS|S) aL Computes empirical quantiles for a data array. Samples quantile are defined by :math:`Q(p) = (1-g).x[i] +g.x[i+1]`, where :math:`x[j]` is the *j*th order statistic, and `i = (floor(n*p+m))`, `m=alpha+p*(1-alpha-beta)` and `g = n*p + m - i`. Typical values of (alpha,beta) are: - (0,1) : *p(k) = k/n* : linear interpolation of cdf (R, type 4) - (.5,.5) : *p(k) = (k+1/2.)/n* : piecewise linear function (R, type 5) - (0,0) : *p(k) = k/(n+1)* : (R type 6) - (1,1) : *p(k) = (k-1)/(n-1)*. In this case, p(k) = mode[F(x[k])]. That's R default (R type 7) - (1/3,1/3): *p(k) = (k-1/3)/(n+1/3)*. Then p(k) ~ median[F(x[k])]. The resulting quantile estimates are approximately median-unbiased regardless of the distribution of x. (R type 8) - (3/8,3/8): *p(k) = (k-3/8)/(n+1/4)*. Blom. The resulting quantile estimates are approximately unbiased if x is normally distributed (R type 9) - (.4,.4) : approximately quantile unbiased (Cunnane) - (.35,.35): APL, used with PWM ?? JP - (0.35, 0.65): PWM ?? JP p(k) = (k-0.35)/n Parameters ---------- a : array_like Input data, as a sequence or array of dimension at most 2. prob : array_like, optional List of quantiles to compute. alpha : float, optional Plotting positions parameter, default is 0.4. beta : float, optional Plotting positions parameter, default is 0.4. axis : int, optional Axis along which to perform the trimming. If None (default), the input array is first flattened. limit : tuple Tuple of (lower, upper) values. Values of `a` outside this closed interval are ignored. Returns ------- quants : MaskedArray An array containing the calculated quantiles. Examples -------- >>> from scipy.stats.mstats import mquantiles >>> a = np.array([6., 47., 49., 15., 42., 41., 7., 39., 43., 40., 36.]) >>> mquantiles(a) array([ 19.2, 40. , 42.8]) Using a 2D array, specifying axis and limit. >>> data = np.array([[ 6., 7., 1.], [ 47., 15., 2.], [ 49., 36., 3.], [ 15., 39., 4.], [ 42., 40., -999.], [ 41., 41., -999.], [ 7., -999., -999.], [ 39., -999., -999.], [ 43., -999., -999.], [ 40., -999., -999.], [ 36., -999., -999.]]) >>> mquantiles(data, axis=0, limit=(0, 50)) array([[ 19.2 , 14.6 , 1.45], [ 40. , 37.5 , 2.5 ], [ 42.8 , 40.05, 3.55]]) >>> data[:, 2] = -999. >>> mquantiles(data, axis=0, limit=(0, 50)) masked_array(data = [[19.2 14.6 --] [40.0 37.5 --] [42.8 40.05 --]], mask = [[False False True] [False False True] [False False True]], fill_value = 1e+20) )probalphapbetapaxislimit fill_valuemaskFcopyndmin?NrTr dtype) isinstancenpr MaskedArrayrmstats mquantilesfillednanisnananyarrayasarrayravelarangendimrollaxissortshapelistemptylenfloatresizefloorclipastypeintslice)ar r r r r masknanmarrnanmaskdatapmisrolledxn returnshapealephkindgammaqs i/var/www/dash_apps/app1/venv/lib/python3.12/site-packages/statsmodels/sandbox/stats/stats_mstats_short.py quantilesrF&sl!RUU&&'||&&qtF&W['  ||&&qtF&W['yy"&&11((1+ ;;=88AG,D<<**4d6QW#'u+6D99Tbff5 5 ::a=D E+ABvIeO$$AH zz|yy#D){{4& 1A  Atzz"KK AvxxAe,, ayyAGG$$ qS1WE Aqs#$++C0A &-C 4[CF 1WNN1Q  $E E1QqS6E!A$J&A{{1aa((c tj|t}|dkjs|dkDjrt d|zt ||dz g|||||j S)zCalculate the score at the given 'per' percentile of the sequence a. For example, the score at per=50 is the median. This function is a shortcut to mquantile rgY@z7The percentile should be between 0. and 100. ! (got %s))r r r r r r6)rr$r.r" ValueErrorrFsqueeze)r9perr r r r r6s rEscoreatpercentilerLst **S% C a}}3:**,%'*+, , TT 6!g ??FwyIrGct|tjjre||jdk(r"t j j|||Stjt j j||||S|rtj|}|jrtj||}||jdk(r#t j j|||}n2tjt j j||||}tj|tjStj|}|jdk(rtj |}d}||j#}d}|j$|}|jdk(r`tj&|j$t(}tj*d|dz|z |dz|z |z z ||j-<|S|j-|j-|dz|z |dz|z |z z }|S)aZReturns the plotting positions (or empirical percentile points) for the data. Plotting positions are defined as (i-alpha)/(n+1-alpha-beta), where: - i is the rank order statistics (starting at 1) - n is the number of unmasked values along the given axis - alpha and beta are two parameters. Typical values for alpha and beta are: - (0,1) : *p(k) = k/n* : linear interpolation of cdf (R, type 4) - (.5,.5) : *p(k) = (k-1/2.)/n* : piecewise linear function (R, type 5) (Bliss 1967: "Rankit") - (0,0) : *p(k) = k/(n+1)* : Weibull (R type 6), (Van der Waerden 1952) - (1,1) : *p(k) = (k-1)/(n-1)*. In this case, p(k) = mode[F(x[k])]. That's R default (R type 7) - (1/3,1/3): *p(k) = (k-1/3)/(n+1/3)*. Then p(k) ~ median[F(x[k])]. The resulting quantile estimates are approximately median-unbiased regardless of the distribution of x. (R type 8), (Tukey 1962) - (3/8,3/8): *p(k) = (k-3/8)/(n+1/4)*. The resulting quantile estimates are approximately unbiased if x is normally distributed (R type 9) (Blom 1958) - (.4,.4) : approximately quantile unbiased (Cunnane) - (.35,.35): APL, used with PWM Parameters ---------- x : sequence Input data, as a sequence or array of dimension at most 2. prob : sequence List of quantiles to compute. alpha : {0.4, float} optional Plotting positions parameter. beta : {0.4, float} optional Plotting positions parameter. Notes ----- I think the adjustments assume that there are no ties in order to be a reasonable approximation to a continuous density function. TODO: check this References ---------- unknown, dates to original papers from Beasley, Erickson, Allison 2009 Behav Genet ralphabetarrrrr)rrrrr'rrplotting_positionsapply_along_axisr!r"r#rr r$size atleast_1dr%r*r,r.r&argsort) r9rOrPr r6r8r7r>plposs rErQrQsZ$))* <499><<224u42P P&&u||'F'FdZ_fjk k((4. ;;=88Dw/D|tyyA~||66t5t6T**5<<+J+JDRV^cjno99Tbff5 5 ::d D yyA~}}T" |zz| 4A yyA~51!#1QqS!1E!9AbDJtO Ldlln Ld#++D1B6>2eDQ LrGcFtj|}|jdkDr td| tj|j }nAtj |tdd}|j |j k7r tdt|}|j}||j}tj|j } |dk(r"d|z|dz |z|z |dz|z |z z | |<| Sd|z|z |ddz|z |z z | |<| S) aWeighted plotting positions (or empirical percentile points) for the data. observations are weighted and the plotting positions are defined as (ws-alpha)/(n-alpha-beta), where: - ws is the weighted rank order statistics or cumulative weighted sum, normalized to n if method is "normed" - n is the number of values along the given axis if method is "normed" and total weight otherwise - alpha and beta are two parameters. wtd.quantile in R package Hmisc seems to use the "notnormed" version. notnormed coincides with unweighted segment in example, drop "normed" version ? See Also -------- plotting_positions : unweighted version that works also with more than one dimension and has other options rz!currently implemented only for 1dFrz9if weights is given, it needs to be the sameshape as datanormedr) rrTr'rIonesr*r#r.r-rUcumsumr,) r9weightsrOrPmethodr=r>xargsortwsress rEplotting_positions_w1dra s, dAvvz<==''!''"((7EQ? ==AGG #-. . AAyy{H   ! ! #B ((177 C Br"va-"U 4@H  JBur"vbyt';<H JrGchddlm}t|||dd}|jj |}|S)z.rank based normal inverse transformed cdf rrF)rOrPr r6)scipyrrQnormppf)r=rOrPr rranks ranks_transfs rEedf_normal_inverse_transformedrh7s1 qE5 QE::>>%(L rG__main__ rYrr)rr)r6)rrNrY)r r6)rrlgffffff?g?rNgffffff$@Z)rrrlrrz"ppf, cdf values on horizontal axis0)r\r]post)wherez-oz cdf, cdf values on vertical axis)rrrrN)rrrF)Nrr notnormed)?rsr)/__doc__numpyrrrcrr+rFrLrQmeppfrarh__name__r&r=printreshaper#xmr2r.x2r r4sl1allrr fix_invalidaxdstackTx3testing assert_equalw1 plotexamplematplotlib.pyplotpyplotpltfiguretitlesteprepeatplotshowrrGrErs.<(2DHT IKZ ?B"-(T z ! A Q   " b#A Q   )AA  )AD !" )AA  !B %BffBsG Ra ()d Qm !"SU),0B1SU80LLQQST yCE#y3q5'::??AB u||&&~r~~bQi'@AYrRUVWRWybcEddiiklm q !"2.2DQR2PPUUWX y"%12)>>CCEF u||&&~r~~b'9&CyQSZ\fgGhhmmopq  5<< * *>2>>"+= >BTUW^blmBn n s s uv Aa5   B` !"2.q15GRTUVRV5WW\\^_`JJ.yryy}DvVYZ[d[][d[deg[hYhimYmoqXqrJJ.yryy}CcRUVW`WYW`W`acWdUdehUhkqTrsJJ.yryy}=)"))B-PS@SV\?]^ "I A2w '( 1Q3 () !!AaC& )-?!A#-G G L L NO BK'  67'!A#3G1Q3W]^001QqS6"!1LMibiiXYZ[\]Z]X^_aghNipvw'!A#3G1Q3QUV001QqS6"!1LMibiiXYZ[\]Z]X^_aghNikop  451Q3/!A#3OV\]1QqS6"!,ell.M.MibiiXYZ[\]Z]X^_aghNi.jqwx1Q3/!A#3OQUV1QqS6"!,ell.M.MibiiXYZ[\]Z]X^_aghNi.jlpq CHHJ{rG