{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The Dirichlet distribution is a distribution over vectors " }, { "__type": "InlineMath", "__tag": 4057, "value": "x" }, { "__type": "Text", "__tag": 4046, "value": " that fulfil the conditions " }, { "__type": "InlineMath", "__tag": 4057, "value": "x_i>0" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineMath", "__tag": 4057, "value": "\\sum_{i=1}^k x_i = 1" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The probability density function " }, { "__type": "InlineMath", "__tag": 4057, "value": "p" }, { "__type": "Text", "__tag": 4046, "value": " of a Dirichlet-distributed random vector " }, { "__type": "InlineMath", "__tag": 4057, "value": "X" }, { "__type": "Text", "__tag": 4046, "value": " is proportional to" } ] }, { "__type": "Math", "__tag": 4058, "value": "p(x) \\propto \\prod_{i=1}^{k}{x^{\\alpha_i-1}_i}," }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "where " }, { "__type": "InlineMath", "__tag": 4057, "value": "\\alpha" }, { "__type": "Text", "__tag": 4046, "value": " is a vector containing the positive concentration parameters." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The method uses the following property for computation: let " }, { "__type": "InlineMath", "__tag": 4057, "value": "Y" }, { "__type": "Text", "__tag": 4046, "value": " be a random vector which has components that follow a standard gamma distribution, then " }, { "__type": "InlineMath", "__tag": 4057, "value": "X = \\frac{1}{\\sum_{i=1}^k{Y_i}} Y" }, { "__type": "Text", "__tag": 4046, "value": " is Dirichlet-distributed" } ] } ], "title": [], "level": 0, "target": null }, "Warns": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Raises": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "", "annotation": "ValueError", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If any value in " }, { "__type": "InlineCode", "__tag": 4051, "value": "alpha" }, { "__type": "Text", "__tag": 4046, "value": " is less than zero" } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Yields": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Methods": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Returns": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "samples", "annotation": "ndarray,", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The drawn samples, of shape " }, { "__type": "InlineCode", "__tag": 4051, "value": "(size, k)" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Draw samples from the Dirichlet distribution." } ] } ], "title": [], "level": 0, "target": null }, "Receives": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Warnings": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Attributes": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Parameters": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "alpha", "annotation": "sequence of floats, length k", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Parameter of the distribution (length " }, { "__type": "InlineCode", "__tag": 4051, "value": "k" }, { "__type": "Text", "__tag": 4046, "value": " for sample of length " }, { "__type": "InlineCode", "__tag": 4051, "value": "k" }, { "__type": "Text", "__tag": 4046, "value": ")." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "size", "annotation": "int or tuple of ints, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Output shape. 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[1] David McKay, \"Information Theory, Inference and Learning", " Algorithms,\" chapter 23,", " https://www.inference.org.uk/mackay/itila/", ".. [2] Wikipedia, \"Dirichlet distribution\",", " https://en.wikipedia.org/wiki/Dirichlet_distribution" ], "qa": "numpy.random._generator:Generator.dirichlet", "arbitrary": [], "local_refs": [ "alpha", "samples", "size" ] }