{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The implementation of " }, { "__type": "InlineRole", "__tag": 4003, "value": "theilslopes", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " follows " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "1" }, { "__type": "Text", "__tag": 4046, "value": ". The intercept is not defined in " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "1" }, { "__type": "Text", "__tag": 4046, "value": ", and here it is defined as " }, { "__type": "InlineCode", "__tag": 4051, "value": "median(y) - slope*median(x)" }, { "__type": "Text", "__tag": 4046, "value": ", which is given in " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "3" }, { "__type": "Text", "__tag": 4046, "value": ". 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It computes the slope as the median of all slopes between paired values." } ] } ], "title": [], "level": 0, "target": null }, "Other Parameters": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null } }, "_ordered_sections": [ "Summary", "Extended Summary", "Parameters", "Attributes", "Methods", "Returns", "Yields", "Receives", "Other Parameters", "Raises", "Warns", "Warnings", "Notes" ], "item_file": "/scipy/stats/_stats_mstats_common.py", "item_line": 23, "item_type": "function", "aliases": [ "scipy.stats.theilslopes" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": "import numpy as np\nfrom scipy import stats\nimport matplotlib.pyplot as plt\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "x = np.linspace(-5, 5, num=150)\ny = x + np.random.normal(size=x.size)\ny[11:15] += 10 # add outliers\ny[-5:] -= 7\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nCompute the slope, intercept and 90% confidence interval. For comparison,\nalso compute the least-squares fit with `linregress`:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "res = stats.theilslopes(y, x, 0.90, method='separate')\nlsq_res = stats.linregress(x, y)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nPlot the results. The Theil-Sen regression line is shown in red, with the\ndashed red lines illustrating the confidence interval of the slope (note\nthat the dashed red lines are not the confidence interval of the regression\nas the confidence interval of the intercept is not included). The green\nline shows the least-squares fit for comparison.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "fig = plt.figure()\nax = fig.add_subplot(111)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "ax.plot(x, y, 'b.')\nax.plot(x, res[1] + res[0] * x, 'r-')\nax.plot(x, res[1] + res[2] * x, 'r--')\nax.plot(x, res[1] + res[3] * x, 'r--')\nax.plot(x, lsq_res[1] + lsq_res[0] * x, 'g-')\n", "execution_status": "failure" }, { "__type": "Code", "__tag": 4050, "value": "plt.show()\n", "execution_status": "success" }, { "__type": "Figure", "__tag": 4024, "value": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "1.17.1", "kind": "assets", "path": "fig-481fde80ccf938b5.png" } } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "siegelslopes", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "siegelslopes" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "a similar technique using repeated medians" } ] } ], "type": "func" } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "y", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "x", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "alpha", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "0.95" }, { "__type": "SigParam", "__tag": 4030, "name": "method", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "separate" }, { "__type": "SigParam", "__tag": 4030, "name": "axis", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "nan_policy", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "propagate" }, { "__type": "SigParam", "__tag": 4030, "name": "keepdims", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "False" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "theilslopes" }, "references": [ ".. [1] P.K. Sen, \"Estimates of the regression coefficient based on", " Kendall's tau\", J. Am. Stat. Assoc., Vol. 63, pp. 1379-1389, 1968.", ".. [2] H. Theil, \"A rank-invariant method of linear and polynomial", " regression analysis I, II and III\", Nederl. Akad. Wetensch., Proc.", " 53:, pp. 386-392, pp. 521-525, pp. 1397-1412, 1950.", ".. [3] W.L. Conover, \"Practical nonparametric statistics\", 2nd ed.,", " John Wiley and Sons, New York, pp. 493.", ".. [4] https://en.wikipedia.org/wiki/Theil%E2%80%93Sen_estimator" ], "qa": "scipy.stats._stats_mstats_common:theilslopes", "arbitrary": [], "local_refs": [ "alpha", "axis", "keepdims", "method", "nan_policy", "result", "x", "y" ] }