{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Strong", "__tag": 4048, "children": [ { "__type": "Text", "__tag": 4046, "value": "Array API Standard Support" } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "boxcox_normmax", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._morestats:boxcox_normmax" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable " }, { "__type": "InlineCode", "__tag": 4051, "value": "SCIPY_ARRAY_API=1" }, { "__type": "Text", "__tag": 4046, "value": " and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported." } ] }, { "__type": "Code", "__tag": 4050, "value": "==================== ==================== ====================\nLibrary CPU GPU\n==================== ==================== ====================\nNumPy ✅ n/a \nCuPy n/a ⛔ \nPyTorch ⛔ ⛔ \nJAX ⛔ ⛔ \nDask ⛔ n/a \n==================== ==================== ====================", "execution_status": null }, { "__type": "Blockquote", "__tag": 4059, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "See " }, { "__type": "InlineRole", "__tag": 4003, "value": "dev-arrayapi", "domain": null, "role": "ref", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " for more information." } ] } ] } ], "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": "maxlog", "annotation": "float or ndarray", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The optimal transform parameter found. An array instead of a scalar for " }, { "__type": "InlineCode", "__tag": 4051, "value": "method='all'" }, { "__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": "Compute optimal Box-Cox transform parameter for input data." } ] } ], "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": "x", "annotation": "array_like", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Input array. All entries must be positive, finite, real numbers." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "brack", "annotation": "2-tuple, optional, default (-2.0, 2.0)", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The starting interval for a downhill bracket search for the default " }, { "__type": "CrossRef", "__tag": 4002, "value": "optimize.brent", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.optimize._optimize:brent" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " solver. Note that this is in most cases not critical; the final result is allowed to be outside this bracket. If " }, { "__type": "ParamRef", "__tag": 4071, "name": "optimizer" }, { "__type": "Text", "__tag": 4046, "value": " is passed, " }, { "__type": "ParamRef", "__tag": 4071, "name": "brack" }, { "__type": "Text", "__tag": 4046, "value": " must be None." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "method", "annotation": "str, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The method to determine the optimal transform parameter (" }, { "__type": "InlineRole", "__tag": 4003, "value": "boxcox", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": " " }, { "__type": "InlineCode", "__tag": 4051, "value": "lmbda" }, { "__type": "Text", "__tag": 4046, "value": " parameter). Options are:" } ] }, { "__type": "DefList", "__tag": 4033, "children": [ { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "'pearsonr' (default)" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Maximizes the Pearson correlation coefficient between " }, { "__type": "InlineCode", "__tag": 4051, "value": "y = boxcox(x)" }, { "__type": "Text", "__tag": 4046, "value": " and the expected values for " }, { "__type": "InlineCode", "__tag": 4051, "value": "y" }, { "__type": "Text", "__tag": 4046, "value": " if " }, { "__type": "ParamRef", "__tag": 4071, "name": "x" }, { "__type": "Text", "__tag": 4046, "value": " would be normally-distributed." } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "'mle'" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Maximizes the log-likelihood " }, { "__type": "CrossRef", "__tag": 4002, "value": "boxcox_llf", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._morestats:boxcox_llf" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": ". This is the method used in " }, { "__type": "InlineRole", "__tag": 4003, "value": "boxcox", "domain": null, "role": null, "inventory": null }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] }, { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "'all'" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Use all optimization methods available, and return all results. Useful to compare different methods." } ] } ] } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "optimizer", "annotation": "callable, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "ParamRef", "__tag": 4071, "name": "optimizer" }, { "__type": "Text", "__tag": 4046, "value": " is a callable that accepts one argument:" } ] }, { "__type": "DefList", "__tag": 4033, "children": [ { "__type": "DefListItem", "__tag": 4037, "dt": { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "fun" } ] }, "dd": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "fun" } ] } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "and returns an object, such as an instance of " }, { "__type": "CrossRef", "__tag": 4002, "value": "scipy.optimize.OptimizeResult", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "*", "kind": "api", "path": "scipy.optimize._optimize:OptimizeResult" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": ", which holds the optimal value of " }, { "__type": "CrossRef", "__tag": 4002, "value": "lmbda", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.special._basic:lmbda" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " in an attribute " }, { "__type": "ParamRef", "__tag": 4071, "name": "x" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "See the example below or the documentation of " }, { "__type": "CrossRef", "__tag": 4002, "value": "scipy.optimize.minimize_scalar", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "*", "kind": "api", "path": "scipy.optimize._minimize:minimize_scalar" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " for more information." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "ymax", "annotation": "float, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The unconstrained optimal transform parameter may cause Box-Cox transformed data to have extreme magnitude or even overflow. This parameter constrains MLE optimization such that the magnitude of the transformed " }, { "__type": "ParamRef", "__tag": 4071, "name": "x" }, { "__type": "Text", "__tag": 4046, "value": " does not exceed " }, { "__type": "ParamRef", "__tag": 4071, "name": "ymax" }, { "__type": "Text", "__tag": 4046, "value": ". The default is the maximum value of the input dtype. If set to infinity, " }, { "__type": "CrossRef", "__tag": 4002, "value": "boxcox_normmax", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._morestats:boxcox_normmax" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " returns the unconstrained optimal lambda. Ignored when " }, { "__type": "InlineCode", "__tag": 4051, "value": "method='pearsonr'" }, { "__type": "Text", "__tag": 4046, "value": "." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [], "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": "/scipy/stats/_morestats.py", "item_line": 1235, "item_type": "function", "aliases": [ "scipy.stats.boxcox_normmax" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": "import numpy as np\nfrom scipy import stats\nimport matplotlib.pyplot as plt\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nWe can generate some data and determine the optimal ``lmbda`` in various\nways:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "rng = np.random.default_rng()\nx = stats.loggamma.rvs(5, size=30, random_state=rng) + 5\ny, lmax_mle = stats.boxcox(x)\nlmax_pearsonr = stats.boxcox_normmax(x)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "lmax_mle\nlmax_pearsonr\nstats.boxcox_normmax(x, method='all')\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "fig = plt.figure()\nax = fig.add_subplot(111)\nprob = stats.boxcox_normplot(x, -10, 10, plot=ax)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "ax.axvline(lmax_mle, color='r')\nax.axvline(lmax_pearsonr, color='g', ls='--')\n", "execution_status": "failure" }, { "__type": "Text", "__tag": 4046, "value": "\n" }, { "__type": "Code", "__tag": 4050, "value": "plt.show()\n", "execution_status": "success" }, { "__type": "Figure", "__tag": 4024, "value": { "__type": "RefInfo", "__tag": 4000, "module": "scipy", "version": "1.17.1", "kind": "assets", "path": "fig-2a0c5e68a3ae5e78.png" } }, { "__type": "Text", "__tag": 4046, "value": "\nAlternatively, we can define our own `optimizer` function. Suppose we\nare only interested in values of `lmbda` on the interval [6, 7], we\nwant to use `scipy.optimize.minimize_scalar` with ``method='bounded'``,\nand we want to use tighter tolerances when optimizing the log-likelihood\nfunction. To do this, we define a function that accepts positional argument\n`fun` and uses `scipy.optimize.minimize_scalar` to minimize `fun` subject\nto the provided bounds and tolerances:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "from scipy import optimize\noptions = {'xatol': 1e-12} # absolute tolerance on `x`\ndef optimizer(fun):\n return optimize.minimize_scalar(fun, bounds=(6, 7),\n method=\"bounded\", options=options)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "stats.boxcox_normmax(x, optimizer=optimizer)\n", "execution_status": "failure" } ], "title": [], "level": 0, "target": null }, "see_also": [ { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "boxcox", "reference": { "__type": "RefInfo", "__tag": 4000, "module": "current-module", "version": "current-version", "kind": "to-resolve", "path": "boxcox" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "boxcox_llf", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._morestats:boxcox_llf" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "boxcox_normplot", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.stats._morestats:boxcox_normplot" }, "kind": "module" }, "descriptions": [], "type": "func" }, { "__type": "SeeAlsoItem", "__tag": 4028, "name": { "__type": "CrossRef", "__tag": 4002, "value": "scipy.optimize.minimize_scalar", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.optimize._minimize:minimize_scalar" }, "kind": "module" }, "descriptions": [], "type": "func" } ], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "x", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "brack", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "method", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "pearsonr" }, { "__type": "SigParam", "__tag": 4030, "name": "optimizer", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "POSITIONAL_OR_KEYWORD", "default": "None" }, { "__type": "SigParam", "__tag": 4030, "name": "ymax", "annotation": { "__type": "Empty", "__tag": 4031 }, "kind": "KEYWORD_ONLY", "default": "BIG_FLOAT" } ], "return_annotation": { "__type": "Empty", "__tag": 4031 }, "target_name": "boxcox_normmax" }, "references": null, "qa": "scipy.stats._morestats:boxcox_normmax", "arbitrary": [], "local_refs": [ "brack", "maxlog", "method", "optimizer", "x", "ymax" ] }