-i SSKrSSKJr SSKJrJrJr SSKJ r S/r Sr Sr Sr S r\ "\S S \S S S 9SSSS.Sj5rg)N)stats) _SimpleNormalSignificanceResult _get_pvalue)_axis_nan_policy_factory chatterjeexic URSn[R"USS9n[R"XA5upA[R"XSS9n[ R "USSS9n[ R "U*SSS9n[R"[R"[R"USS95SS9nU(aSSU-US-S- - - nO'S[R"X6- U-SS9-n SX7-U - - nXU4$)Naxismax)methodr ) shapenpargsortbroadcast_arraystake_along_axisrrankdatasumabsdiff) xy y_continuousnjrlnum statisticdens K/var/www/html/venv/lib/python3.13/site-packages/scipy/stats/_correlation.py _xi_statisticr&s  A 12A  q $DA 1b)A qR0A r%b1A &&+,2 6CC16A:.. "&&!%12..# % ?c [R"URS5nU(a-[R"S5[R"U5- $[R"SUS-5n[R "USS9n[R "USS9nSUS-- [R"SU-SU-- S-US--SS9-nSUS-- [R"XcU- U--S-SS9-nSUS-- [R"SU-SU-- S-U-SS9-n SUS-- [R"XU- -SS9-n USU-- U S--U S-- n [R"U 5[R"U5- $) Nr g?rr rr)rfloat64rsqrtarangesortcumsumr) r r!rriuvanbncndntau2s r%_xi_stdr8*sa 1772;Awwu~ ** !QUA A !"A QTBFFAaC!A#IMQT1; ;B QTBFFAQ MA-B7 7B QTBFFAaC!A#IMQ.R8 8B QTBFFAQKr2 2B 2IA Q &D 774=2771: %%r'cUS;a [S5e[U[R5(d#UR 5nSnUS:wa [U5eX4$)N>FTz`y_continuous` must be boolean.z@`method` must be 'asymptotic' or a `PermutationMethod` instance. asymptotic) ValueError isinstancerPermutationMethodlower)rrmessages r%_chatterjeexi_ivr@DsW=(:;; fe55 6 6T \ !W% %  r'c2URUR4$)N)r#pvalue)res_s r%_unpackrETs ==#** $$r'Trr)paired n_samplesresult_to_tuple n_outputs too_smallFr:)r rrc^^[TU5umnSnUS:Xa3[TUT5upgn[XxT5n [5n [ Xi- XS9n Oi[ U[ R5(aJ[ R"S U4UU4SjUSS.UR5DSS0D6n U RU Rp[WW 5$) ah Compute the xi correlation and perform a test of independence The xi correlation coefficient is a measure of association between two variables; the value tends to be close to zero when the variables are independent and close to 1 when there is a strong association. Unlike other correlation coefficients, the xi correlation is effective even when the association is not monotonic. Parameters ---------- x, y : array-like The samples: corresponding observations of the independent and dependent variable. The (N-d) arrays must be broadcastable. axis : int, default: 0 Axis along which to perform the test. method : 'asymptotic' or `PermutationMethod` instance, optional Selects the method used to calculate the *p*-value. Default is 'asymptotic'. The following options are available. * ``'asymptotic'``: compares the standardized test statistic against the normal distribution. * `PermutationMethod` instance. In this case, the p-value is computed using `permutation_test` with the provided configuration options and other appropriate settings. y_continuous : bool, default: False Whether `y` is assumed to be drawn from a continuous distribution. If `y` is drawn from a continuous distribution, results are valid whether this is assumed or not, but enabling this assumption will result in faster computation and typically produce similar results. Returns ------- res : SignificanceResult An object containing attributes: statistic : float The xi correlation statistic. pvalue : float The associated *p*-value: the probability of a statistic at least as high as the observed value under the null hypothesis of independence. See Also -------- scipy.stats.pearsonr, scipy.stats.spearmanr, scipy.stats.kendalltau Notes ----- There is currently no special handling of ties in `x`; they are broken arbitrarily by the implementation. [1]_ notes that the statistic is not symmetric in `x` and `y` *by design*: "...we may want to understand if :math:`Y` is a function :math:`X`, and not just if one of the variables is a function of the other." See [1]_ Remark 1. References ---------- .. [1] Chatterjee, Sourav. "A new coefficient of correlation." Journal of the American Statistical Association 116.536 (2021): 2009-2022. :doi:`10.1080/01621459.2020.1758115`. Examples -------- Generate perfectly correlated data, and observe that the xi correlation is nearly 1.0. >>> import numpy as np >>> from scipy import stats >>> rng = np.random.default_rng(348932549825235) >>> x = rng.uniform(0, 10, size=100) >>> y = np.sin(x) >>> res = stats.chatterjeexi(x, y) >>> res.statistic np.float64(0.9012901290129013) The probability of observing such a high value of the statistic under the null hypothesis of independence is very low. >>> res.pvalue np.float64(2.2206974648177804e-46) As noise is introduced, the correlation coefficient decreases. >>> noise = rng.normal(scale=[[0.1], [0.5], [1]], size=(3, 100)) >>> res = stats.chatterjeexi(x, y + noise, axis=-1) >>> res.statistic array([0.79507951, 0.41824182, 0.16651665]) Because the distribution of `y` is continuous, it is valid to pass ``y_continuous=True``. The statistic is identical, and the p-value (not shown) is only slightly different. >>> stats.chatterjeexi(x, y + noise, y_continuous=True, axis=-1).statistic array([0.79507951, 0.41824182, 0.16651665]) greaterr:) alternativec$>[TUT5S$)Nr)r&)rr rrs r%chatterjeexi..sq!\1RST1Ur'pairings)datar#rMpermutation_typer r ) r@r&r8rrr<rr=permutation_test_asdictr#rBr) rrr rrrMxir r!stdnormrBrCs ` ` r%rrXsJ,L&AL& K  A|4qaL)RXtE FE33 4 4$$!U#jEKNNDT  ]]CJJF b& ))r')numpyrscipyrscipy.stats._stats_pyrrrscipy.stats._axis_nan_policyr__all__r&r8r@rErrTr'r%r_sdPPA  8&4  %,TQ*1Q!M u\x*Mx*r'