{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Warns": { "__type": "Section", "__tag": 4015, "children": [], "title": [], "level": 0, "target": null }, "Raises": { "__type": "Section", "__tag": 4015, "children": [], "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 exponential distribution." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Draw samples from an exponential 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": "scale", "annotation": "float or array_like of floats", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The scale parameter, " }, { "__type": "InlineMath", "__tag": 4057, "value": "\\beta = 1/\\lambda" }, { "__type": "Text", "__tag": 4046, "value": ". 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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": "Its probability density function is" } ] }, { "__type": "Math", "__tag": 4058, "value": "f(x; \\frac{1}{\\beta}) = \\frac{1}{\\beta} \\exp(-\\frac{x}{\\beta})," }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "for " }, { "__type": "InlineCode", "__tag": 4051, "value": "x > 0" }, { "__type": "Text", "__tag": 4046, "value": " and 0 elsewhere. " }, { "__type": "InlineMath", "__tag": 4057, "value": "\\beta" }, { "__type": "Text", "__tag": 4046, "value": " is the scale parameter, which is the inverse of the rate parameter " }, { "__type": "InlineMath", "__tag": 4057, "value": "\\lambda = 1/\\beta" }, { "__type": "Text", "__tag": 4046, "value": ". The rate parameter is an alternative, widely used parameterization of the exponential distribution " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "3" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The exponential distribution is a continuous analogue of the geometric distribution. It describes many common situations, such as the size of raindrops measured over many rainstorms " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "1" }, { "__type": "Text", "__tag": 4046, "value": ", or the time between page requests to Wikipedia " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "2" }, { "__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.Generator.exponential" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Text", "__tag": 4046, "value": "Assume a company has 10000 customer support agents and the time\nbetween customer calls is exponentially distributed and that the\naverage time between customer calls is 4 minutes.\n\n" }, { "__type": "Code", "__tag": 4050, "value": "scale, size = 4, 10000\nrng = np.random.default_rng()\ntime_between_calls = rng.exponential(scale=scale, size=size)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nWhat is the probability that a customer will call in the next\n4 to 5 minutes?\n\n" }, { "__type": "Code", "__tag": 4050, "value": "x = ((time_between_calls < 5).sum())/size\ny = ((time_between_calls < 4).sum())/size\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "x - y\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\nThe corresponding distribution can be visualized as follows:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "import matplotlib.pyplot as plt\nscale, size = 4, 10000\nrng = np.random.default_rng()\nsample = rng.exponential(scale=scale, size=size)\ncount, bins, _ = plt.hist(sample, 30, density=True)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "plt.plot(bins, scale**(-1)*np.exp(-scale**-1*bins), linewidth=2, color='r')\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": "2.5.0.dev0+git20251130.2de293a", "kind": "assets", "path": "fig-abf1b5f9efb4f64f.png" } } ], "title": [], "level": 0, "target": null }, "see_also": [], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "scale", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "1.0" }, { "__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": "exponential" }, "references": [ ".. [1] Peyton Z. Peebles Jr., \"Probability, Random Variables and", " Random Signal Principles\", 4th ed, 2001, p. 57.", ".. [2] Wikipedia, \"Poisson process\",", " https://en.wikipedia.org/wiki/Poisson_process", ".. [3] Wikipedia, \"Exponential distribution\",", " https://en.wikipedia.org/wiki/Exponential_distribution" ], "qa": "numpy.random._generator:Generator.exponential", "arbitrary": [], "local_refs": [ "out", "scale", "size" ] }