{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The probability density function is" } ] }, { "__type": "Math", "__tag": 4058, "value": "P(x; a) = ax^{a-1}, 0 \\le x \\le 1, a>0." }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The power function distribution is just the inverse of the Pareto distribution. It may also be seen as a special case of the Beta distribution." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "It is used, for example, in modeling the over-reporting of insurance claims." } ] } ], "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 a <= 0." } ] } ] } ] } ], "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": "out", "annotation": "ndarray or scalar", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Drawn samples from the parameterized power distribution." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Draws samples in [0, 1] from a power distribution with positive exponent a - 1." } ] } ], "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": "a", "annotation": "float or array_like of floats", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Parameter of the distribution. 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please see the " }, { "__type": "InlineRole", "__tag": 4003, "value": "random-quick-start", "domain": null, "role": "ref", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] } ], "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": null, "item_line": null, "item_type": "cython_function_or_method", "aliases": [ "numpy.random.power", "numpy.random.RandomState.power" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "Draw samples from the distribution:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "a = 5. # shape\nsamples = 1000\ns = np.random.power(a, samples)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nDisplay the histogram of the samples, along with\nthe probability density function:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import matplotlib.pyplot as plt\ncount, bins, ignored = plt.hist(s, bins=30)\nx = np.linspace(0, 1, 100)\ny = a*x**(a-1.)\nnormed_y = samples*np.diff(bins)[0]*y\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "plt.plot(x, normed_y)\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": "numpy", "version": "2.4.4", "kind": "assets", "path": "fig-34c65c3afb03b3ff.png" } }, { "__type": "Text", "__tag": 4046, "value": "\nCompare the power function distribution to the inverse of the Pareto.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "rvs = np.random.power(5, 1000000)\nrvsp = np.random.pareto(5, 1000000)\nxx = np.linspace(0,1,100)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "plt.figure()\nplt.hist(rvs, bins=50, density=True)\nplt.title('np.random.power(5)')\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "plt.figure()\nplt.hist(1./(1.+rvsp), bins=50, density=True)\nplt.title('inverse of 1 + np.random.pareto(5)')\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "plt.figure()\nplt.hist(1./(1.+rvsp), bins=50, density=True)\nplt.title('inverse of stats.pareto(5)')\n", "execution_status": "failure" } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "random.Generator.power", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "random.Generator.power" }, "kind": "module" }, "descriptions": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "which should be used for new code." } ] } ], "type": null } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "a", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "size", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "power" }, "references": [ ".. [1] Christian Kleiber, Samuel Kotz, \"Statistical size distributions", " in economics and actuarial sciences\", Wiley, 2003.", ".. [2] Heckert, N. A. and Filliben, James J. \"NIST Handbook 148:", " Dataplot Reference Manual, Volume 2: Let Subcommands and Library", " Functions\", National Institute of Standards and Technology", " Handbook Series, June 2003.", " https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf" ], "qa": "numpy.random:RandomState.power", "arbitrary": [], "local_refs": [ "a", "out", "size" ] }