IR-e.ddlZddgZddgiZdZddZdS) Njackknife_resamplingjackknife_statsscipyc|jd}|dkrtdtj||dz g}t |D]}tj||||<|S)aPerforms jackknife resampling on numpy arrays. Jackknife resampling is a technique to generate 'n' deterministic samples of size 'n-1' from a measured sample of size 'n'. Basically, the i-th sample, (1<=i<=n), is generated by means of removing the i-th measurement of the original sample. Like the bootstrap resampling, this statistical technique finds applications in estimating variance, bias, and confidence intervals. Parameters ---------- data : ndarray Original sample (1-D array) from which the jackknife resamples will be generated. Returns ------- resamples : ndarray The i-th row is the i-th jackknife sample, i.e., the original sample with the i-th measurement deleted. References ---------- .. [1] McIntosh, Avery. "The Jackknife Estimation Method". .. [2] Efron, Bradley. "The Jackknife, the Bootstrap, and other Resampling Plans". Technical Report No. 63, Division of Biostatistics, Stanford University, December, 1980. .. [3] Jackknife resampling r+data must contain at least one measurement.)shape ValueErrornpemptyrangedelete)datan resamplesis 7lib/python3.11/site-packages/astropy/stats/jackknife.pyrr sqB 1 AAvvFGGG!QU$$I 1XX**yq)) ! ffffff?c.d|cxkrdksntd|jd}|dkrtdddlm}t |}||}t j|d|}t j|d}|dz ||z z} t j|dz t j||z ||z zdz} || z } t jd||z} | | t j | | fzz} | | | | fS)a9 Performs jackknife estimation on the basis of jackknife resamples. This function requires `SciPy `_ to be installed. Parameters ---------- data : ndarray Original sample (1-D array). statistic : function Any function (or vector of functions) on the basis of the measured data, e.g, sample mean, sample variance, etc. The jackknife estimate of this statistic will be returned. confidence_level : float, optional Confidence level for the confidence interval of the Jackknife estimate. Must be a real-valued number in (0,1). Default value is 0.95. Returns ------- estimate : float or `~numpy.ndarray` The i-th element is the bias-corrected "jackknifed" estimate. bias : float or `~numpy.ndarray` The i-th element is the jackknife bias. std_err : float or `~numpy.ndarray` The i-th element is the jackknife standard error. conf_interval : ndarray If ``statistic`` is single-valued, the first and second elements are the lower and upper bounds, respectively. If ``statistic`` is vector-valued, each column corresponds to the confidence interval for each component of ``statistic``. The first and second rows contain the lower and upper bounds, respectively. Examples -------- 1. Obtain Jackknife resamples: >>> import numpy as np >>> from astropy.stats import jackknife_resampling >>> from astropy.stats import jackknife_stats >>> data = np.array([1,2,3,4,5,6,7,8,9,0]) >>> resamples = jackknife_resampling(data) >>> resamples array([[2., 3., 4., 5., 6., 7., 8., 9., 0.], [1., 3., 4., 5., 6., 7., 8., 9., 0.], [1., 2., 4., 5., 6., 7., 8., 9., 0.], [1., 2., 3., 5., 6., 7., 8., 9., 0.], [1., 2., 3., 4., 6., 7., 8., 9., 0.], [1., 2., 3., 4., 5., 7., 8., 9., 0.], [1., 2., 3., 4., 5., 6., 8., 9., 0.], [1., 2., 3., 4., 5., 6., 7., 9., 0.], [1., 2., 3., 4., 5., 6., 7., 8., 0.], [1., 2., 3., 4., 5., 6., 7., 8., 9.]]) >>> resamples.shape (10, 9) 2. Obtain Jackknife estimate for the mean, its bias, its standard error, and its 95% confidence interval: >>> test_statistic = np.mean >>> estimate, bias, stderr, conf_interval = jackknife_stats( ... data, test_statistic, 0.95) >>> estimate 4.5 >>> bias 0.0 >>> stderr # doctest: +FLOAT_CMP 0.95742710775633832 >>> conf_interval array([2.62347735, 6.37652265]) 3. Example for two estimates >>> test_statistic = lambda x: (np.mean(x), np.var(x)) >>> estimate, bias, stderr, conf_interval = jackknife_stats( ... data, test_statistic, 0.95) >>> estimate array([4.5 , 9.16666667]) >>> bias array([ 0. , -0.91666667]) >>> stderr array([0.95742711, 2.69124476]) >>> conf_interval array([[ 2.62347735, 3.89192387], [ 6.37652265, 14.44140947]]) IMPORTANT: Note that confidence intervals are given as columns rrz#confidence level must be in (0, 1).r)erfinv)axisg@) r r scipy.specialrrr apply_along_axismeansqrtarray)r statisticconfidence_levelrrr stat_data jack_statmean_jack_statbiasstd_errestimatez_score conf_intervals rrr6s^v  $ $ $ $1 $ $ $ $>??? 1 AAvvFGGG%$$$$$$T**I $I#Iq)<r,s_ !#4 5)G95***Z{2{2{2{2{2{2r