{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "With " }, { "__type": "InlineCode", "__tag": 4051, "value": "method=\"MLE\"" }, { "__type": "Text", "__tag": 4046, "value": " (default), the fit is computed by minimizing the negative log-likelihood function. A large, finite penalty (rather than infinite negative log-likelihood) is applied for observations beyond the support of the distribution." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "With " }, { "__type": "InlineCode", "__tag": 4051, "value": "method=\"MM\"" }, { "__type": "Text", "__tag": 4046, "value": ", the fit is computed by minimizing the L2 norm of the relative errors between the first " }, { "__type": "Emphasis", "__tag": 4047, "children": [ { "__type": "Text", "__tag": 4046, "value": "k" } ] }, { "__type": "Text", "__tag": 4046, "value": " raw (about zero) data moments and the corresponding distribution moments, where " }, { "__type": "Emphasis", "__tag": 4047, "children": [ { "__type": "Text", "__tag": 4046, "value": "k" } ] }, { "__type": "Text", "__tag": 4046, "value": " is the number of non-fixed parameters. More precisely, the objective function is " } ] }, { "__type": "Code", "__tag": 4050, "value": "(((data_moments - dist_moments)\n / np.maximum(np.abs(data_moments), 1e-8))**2).sum()", "execution_status": null }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "where the constant " }, { "__type": "InlineCode", "__tag": 4051, "value": "1e-8" }, { "__type": "Text", "__tag": 4046, "value": " avoids division by zero in case of vanishing data moments. Typically, this error norm can be reduced to zero. Note that the standard method of moments can produce parameters for which some data are outside the support of the fitted distribution; this implementation does nothing to prevent this." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "For either method, the returned answer is not guaranteed to be globally optimal; it may only be locally optimal, or the optimization may fail altogether. 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To\nkeep the zero-th shape parameter ``a`` equal 1, use ``f0=1`` or,\nequivalently, ``fa=1``:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "a1, b1, loc1, scale1 = beta.fit(x, fa=1, floc=0, fscale=1)\na1\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nNot all distributions return estimates for the shape parameters.\n``norm`` for example just returns estimates for location and scale:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy.stats import norm\nx = norm.rvs(a, b, size=1000, random_state=123)\nloc1, scale1 = norm.fit(x)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "loc1, scale1\n", "execution_status": "failure" } ], "title": [], "level": 0, "target": null }, "see_also": [], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "self", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "data", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "args", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "VAR_POSITIONAL", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "kwds", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "VAR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "fit" }, "references": null, "qa": "scipy.stats._continuous_distns:weibull_min_gen.fit", "arbitrary": [], "local_refs": [ "**kwds", "...", "arg1", "arg2", "arg3", "data", "parameter_tuple" ] }