{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Public methods of an instance of a distribution class (e.g., " }, { "__type": "InlineCode", "__tag": 4051, "value": "pdf" }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "InlineCode", "__tag": 4051, "value": "cdf" }, { "__type": "Text", "__tag": 4046, "value": ") check their arguments and pass valid arguments to private, computational methods (" }, { "__type": "InlineCode", "__tag": 4051, "value": "_pdf" }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "InlineCode", "__tag": 4051, "value": "_cdf" }, { "__type": "Text", "__tag": 4046, "value": "). For " }, { "__type": "InlineCode", "__tag": 4051, "value": "pdf(x)" }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "InlineCode", "__tag": 4051, "value": "x" }, { "__type": "Text", "__tag": 4046, "value": " is valid if it is within the support of the distribution. 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" }, { "__type": "InlineCode", "__tag": 4051, "value": "x" }, { "__type": "Text", "__tag": 4046, "value": " being in the support interval is equivalent to " }, { "__type": "InlineCode", "__tag": 4051, "value": "self.a <= x <= self.b" }, { "__type": "Text", "__tag": 4046, "value": ". If either of the endpoints of the support do depend on the shape parameters, then i) the distribution must implement the " }, { "__type": "InlineCode", "__tag": 4051, "value": "_get_support" }, { "__type": "Text", "__tag": 4046, "value": " method; and ii) those dependent endpoints must be omitted from the distribution's call to the " }, { "__type": "InlineCode", "__tag": 4051, "value": "rv_continuous" }, { "__type": "Text", "__tag": 4046, "value": " initializer." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Correct, but potentially slow defaults exist for the remaining methods but for speed and/or accuracy you can over-ride " } ] }, { "__type": "Code", "__tag": 4050, "value": "_logpdf, _cdf, _logcdf, _ppf, _rvs, _isf, _sf, _logsf", "execution_status": null, "out": "" }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The default method " }, { "__type": "InlineCode", "__tag": 4051, "value": "_rvs" }, { "__type": "Text", "__tag": 4046, "value": " relies on the inverse of the cdf, " }, { "__type": "InlineCode", "__tag": 4051, "value": "_ppf" }, { "__type": "Text", "__tag": 4046, "value": ", applied to a uniform random variate. 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In this case, " }, { "__type": "ParamRef", "__tag": 4071, "name": "shapes" }, { "__type": "Text", "__tag": 4046, "value": " will be automatically deduced from the signatures of the overridden methods (" }, { "__type": "CrossRef", "__tag": 4002, "value": "pdf", "reference": { "__type": "RefInfo", "__tag": 4000, "module": null, "version": null, "kind": "local", "path": "pdf" }, "kind": "local" }, { "__type": "Text", "__tag": 4046, "value": ", " }, { "__type": "CrossRef", "__tag": 4002, "value": "cdf", "reference": { "__type": "RefInfo", "__tag": 4000, "module": null, "version": null, "kind": "local", "path": "cdf" }, "kind": "local" }, { "__type": "Text", "__tag": 4046, "value": " etc). If, for some reason, you prefer to avoid relying on introspection, you can specify " }, { "__type": "InlineCode", "__tag": 4051, "value": "shapes" }, { "__type": "Text", "__tag": 4046, "value": " explicitly as an argument to the instance constructor." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Strong", "__tag": 4048, "children": [ { "__type": "Text", "__tag": 4046, "value": "Frozen Distributions" } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Normally, you must provide shape parameters (and, optionally, location and scale parameters to each call of a method of a distribution." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Alternatively, the object may be called (as a function) to fix the shape, location, and scale parameters returning a \"frozen\" continuous RV object:" } ] }, { "__type": "DefList", "__tag": 4033, "children": [ { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "rv = generic(, loc=0, scale=1)" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "rv_frozen", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._distn_infrastructure:rv_frozen" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " object with the same methods but holding the given shape, location, and scale fixed" } ] } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Strong", "__tag": 4048, "children": [ { "__type": "Text", "__tag": 4046, "value": "Statistics" } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Statistics are computed using numerical integration by default. For speed you can redefine this using " }, { "__type": "InlineCode", "__tag": 4051, "value": "_stats" }, { "__type": "Text", "__tag": 4046, "value": ":" } ] }, { "__type": "BulletList", "__tag": 4053, "ordered": false, "start": 1, "children": [ { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "take shape parameters and return mu, mu2, g1, g2" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If you can't compute one of these, return it as None" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Can also be defined with a keyword argument " }, { "__type": "InlineCode", "__tag": 4051, "value": "moments" }, { "__type": "Text", "__tag": 4046, "value": ", which is a string composed of \"m\", \"v\", \"s\", and/or \"k\". 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It cannot be used directly as a distribution." } ] } ], "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": "build-install/usr/lib/python3.14/site-packages/scipy/stats/_distn_infrastructure.py", "item_line": 1669, "item_type": "class", "aliases": [ "scipy.stats.rv_continuous" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "To create a new Gaussian distribution, we would do the following:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy.stats import rv_continuous\nclass gaussian_gen(rv_continuous):\n \"Gaussian distribution\"\n def _pdf(self, x):\n return np.exp(-x**2 / 2.) / np.sqrt(2.0 * np.pi)\ngaussian = gaussian_gen(name='gaussian')\n", "execution_status": "success", "out": "" }, { "__type": "Text", "__tag": 4046, "value": "\n``scipy.stats`` distributions are *instances*, so here we subclass\n`rv_continuous` and create an instance. With this, we now have\na fully functional distribution with all relevant methods automagically\ngenerated by the framework.\n\nNote that above we defined a standard normal distribution, with zero mean\nand unit variance. Shifting and scaling of the distribution can be done\nby using ``loc`` and ``scale`` parameters: ``gaussian.pdf(x, loc, scale)``\nessentially computes ``y = (x - loc) / scale`` and\n``gaussian._pdf(y) / scale``." } ], "title": [], "level": 0, "target": null }, "see_also": [], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "momtype", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "1" }, { "__type": "SigParam", "__tag": 4030, "name": "a", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "b", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "xtol", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "1e-14" }, { "__type": "SigParam", "__tag": 4030, "name": "badvalue", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "name", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "longname", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "shapes", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "seed", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "rv_continuous" }, "references": null, "qa": "scipy.stats._distn_infrastructure:rv_continuous", "arbitrary": [], "local_refs": [ "__call__", "a", "b", "badvalue", "cdf", "entropy", "expect", "fit", "fit_loc_scale", "interval", "isf", "logcdf", "logpdf", "logsf", "longname", "mean", "median", "moment", "momtype", "name", "nnlf", "pdf", "ppf", "rvs", "seed", "sf", "shapes", "stats", "std", "support", "var", "xtol" ] }