{ "__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 for the Rayleigh distribution is" } ] }, { "__type": "Math", "__tag": 4058, "value": "P(x;scale) = \\frac{x}{scale^2}e^{\\frac{-x^2}{2 \\cdotp scale^2}}" }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The Rayleigh distribution would arise, for example, if the East and North components of the wind velocity had identical zero-mean Gaussian distributions. 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Otherwise, " }, { "__type": "InlineCode", "__tag": 4051, "value": "np.array(scale).size" }, { "__type": "Text", "__tag": 4046, "value": " samples are drawn." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The " }, { "__type": "InlineMath", "__tag": 4057, "value": "\\chi" }, { "__type": "Text", "__tag": 4046, "value": " and Weibull distributions are generalizations of the Rayleigh." } ] }, { "__type": "Admonition", "__tag": 4056, "kind": "note", "base_type": "note", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "note " } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "New code should use the " }, { "__type": "CrossRef", "__tag": 4002, "value": "rayleigh", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy.random._generator:Generator.rayleigh" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " method of a " }, { "__type": "CrossRef", "__tag": 4002, "value": "Generator", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "numpy", "version": "*", "kind": "api", "path": "numpy.random._generator:Generator" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " instance instead; 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.rayleigh", "numpy.random.RandomState.rayleigh" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "Draw values from the distribution and plot the histogram\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from matplotlib.pyplot import hist\nvalues = hist(np.random.rayleigh(3, 100000), bins=200, density=True)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nWave heights tend to follow a Rayleigh distribution. 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