diff --git a/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/README.md b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/README.md new file mode 100644 index 000000000000..8e7b7ecf2980 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/README.md @@ -0,0 +1,138 @@ + + +# Variance + +> [Bradford][bradford-distribution] distribution [variance][variance]. + + + +
+ +The [variance][variance] for a [Bradford][bradford-distribution] random variable is + + + +```math +\mathop{\mathrm{Var}}\left( X \right) = \frac{(c+2) \ln(1+c) - 2c}{2c (\ln(1+c))^2} +``` + + + + + +where `c` is the shape parameter. + +
+ + + + + +
+ +## Usage + +```javascript +var variance = require( '@stdlib/stats/base/dists/bradford/variance' ); +``` + +#### variance( c ) + +Returns the [variance][variance] of a [Bradford][bradford-distribution] distribution with shape parameter `c`. + +```javascript +var v = variance( 0.1 ); +// returns ~0.083 + +v = variance( 10.0 ); +// returns ~0.076 +``` + +If provided a shape parameter `c <= 0`, the function returns `NaN`. + +```javascript +var v = variance( 0.0 ); +// returns NaN + +v = variance( -1.5 ); +// returns NaN +``` + +
+ + + + + +
+ +
+ + + + + +
+ +## Examples + + + +```javascript +var uniform = require( '@stdlib/random/array/uniform' ); +var variance = require( '@stdlib/stats/base/dists/bradford/variance' ); + +var c = uniform( 10, 0.1, 10.0 ); + +var v; +var i; +for ( i = 0; i < c.length; i++ ) { + v = variance( c[ i ] ); + console.log( 'c: %d, Var(X;c): %d', c[ i ].toFixed( 4 ), v.toFixed( 4 ) ); +} +``` + +
+ + + + + +
+ +
+ + + + + +
+ +[bradford-distribution]: https://en.wikipedia.org/wiki/Bradford%27s_law + +[variance]: https://en.wikipedia.org/wiki/Variance + +
+ + diff --git a/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/benchmark/benchmark.js new file mode 100644 index 000000000000..f55d94a07bb2 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/benchmark/benchmark.js @@ -0,0 +1,52 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var bench = require( '@stdlib/bench' ); +var uniform = require( '@stdlib/random/array/uniform' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var pkg = require( './../package.json' ).name; +var variance = require( './../lib' ); + + +// MAIN // + +bench( pkg, function benchmark( b ) { + var c; + var y; + var i; + + c = uniform( 100, 0.1, 10.0 ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + y = variance( c[ i % c.length ] ); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/img/equation_bradford_variance.svg b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/img/equation_bradford_variance.svg new file mode 100644 index 000000000000..2912c4402b01 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/img/equation_bradford_variance.svg @@ -0,0 +1,72 @@ + +normal upper V times normal a times normal r left-parenthesis upper X right-parenthesis equals StartFraction left-parenthesis c plus 2 right-parenthesis ln left-parenthesis 1 plus c right-parenthesis minus 2 c Over 2 c left-parenthesis ln left-parenthesis 1 plus c right-parenthesis right-parenthesis squared EndFraction + + + \ No newline at end of file diff --git a/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/repl.txt new file mode 100644 index 000000000000..f1f4187329e5 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/repl.txt @@ -0,0 +1,28 @@ + +{{alias}}( c ) + Returns the variance of a Bradford distribution with shape parameter `c`. + + If `c <= 0`, the function returns `NaN`. + + Parameters + ---------- + c: number + Shape parameter. + + Returns + ------- + out: number + Variance. + + Examples + -------- + > var v = {{alias}}( 0.1 ) + ~0.083 + > v = {{alias}}( 0.5 ) + ~0.083 + > v = {{alias}}( 10.0 ) + ~0.076 + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/types/index.d.ts new file mode 100644 index 000000000000..6782e45d6867 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/types/index.d.ts @@ -0,0 +1,60 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2025 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +// TypeScript Version: 4.1 + +/** +* Returns the variance of a Bradford distribution. +* +* ## Notes +* +* - If `c <= 0`, the function returns `NaN`. +* +* @param c - shape parameter +* @returns variance +* +* @example +* var v = variance( 0.1 ); +* // returns ~0.083 +* +* @example +* var v = variance( 0.5 ); +* // returns ~0.083 +* +* @example +* var v = variance( 10.0 ); +* // returns ~0.076 +* +* @example +* var v = variance( 0.0 ); +* // returns NaN +* +* @example +* var v = variance( -1.0 ); +* // returns NaN +* +* @example +* var v = variance( NaN ); +* // returns NaN +*/ +declare function variance( c: number ): number; + + +// EXPORTS // + +export = variance; diff --git a/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/types/test.ts b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/types/test.ts new file mode 100644 index 000000000000..b5396f4675ce --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/docs/types/test.ts @@ -0,0 +1,44 @@ +/* +* @license Apache-2.0 +* +* Copyright (c) 2025 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +import variance = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + variance( 0.3 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided a value other than a number... +{ + variance( true ); // $ExpectError + variance( false ); // $ExpectError + variance( null ); // $ExpectError + variance( undefined ); // $ExpectError + variance( '5' ); // $ExpectError + variance( [] ); // $ExpectError + variance( {} ); // $ExpectError + variance( ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided insufficient arguments... +{ + variance(); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/examples/index.js b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/examples/index.js new file mode 100644 index 000000000000..146daa32d4db --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/examples/index.js @@ -0,0 +1,31 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +var uniform = require( '@stdlib/random/array/uniform' ); +var variance = require( './../lib' ); + +var c = uniform( 10, 0.1, 10.0 ); + +var v; +var i; +for ( i = 0; i < c.length; i++ ) { + v = variance( c[ i ] ); + console.log( 'c: %d, Var(X;c): %d', c[ i ].toFixed( 4 ), v.toFixed( 4 ) ); +} diff --git a/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/lib/index.js b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/lib/index.js new file mode 100644 index 000000000000..e4f6f38e22af --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/lib/index.js @@ -0,0 +1,43 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +/** +* Bradford distribution variance. +* +* @module @stdlib/stats/base/dists/bradford/variance +* +* @example +* var variance = require( '@stdlib/stats/base/dists/bradford/variance' ); +* +* var v = variance( 0.1 ); +* // returns ~0.083 +* +* v = variance( 10.0 ); +* // returns ~0.076 +*/ + +// MODULES // + +var variance = require( './main.js' ); + + +// EXPORTS // + +module.exports = variance; diff --git a/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/lib/main.js new file mode 100644 index 000000000000..c7b41e66bf0a --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/lib/main.js @@ -0,0 +1,74 @@ +/** +* @license Apache-2.0 +* +* Copyright (c) 2025 The Stdlib Authors. +* +* Licensed under the Apache License, Version 2.0 (the "License"); +* you may not use this file except in compliance with the License. +* You may obtain a copy of the License at +* +* http://www.apache.org/licenses/LICENSE-2.0 +* +* Unless required by applicable law or agreed to in writing, software +* distributed under the License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var ln = require( '@stdlib/math/base/special/ln' ); + + +// MAIN // + +/** +* Returns the variance of a Bradford distribution. +* +* @param {PositiveNumber} c - shape parameter +* @returns {PositiveNumber} variance +* +* @example +* var v = variance( 0.1 ); +* // returns ~0.083 +* +* @example +* var v = variance( 0.5 ); +* // returns ~0.083 +* +* @example +* var v = variance( 10.0 ); +* // returns ~0.076 +* +* @example +* var v = variance( 0.0 ); +* // returns NaN +* +* @example +* var v = variance( -1.0 ); +* // returns NaN +* +* @example +* var v = variance( NaN ); +* // returns NaN +*/ +function variance( c ) { + var k; + if ( + isnan( c ) || + c <= 0.0 + ) { + return NaN; + } + k = ln( 1.0 + c ); + return ( ( ( 2.0+c ) * k ) - ( 2.0*c ) ) / ( 2.0*c*k*k ); +} + + +// EXPORTS // + +module.exports = variance; diff --git a/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/package.json b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/package.json new file mode 100644 index 000000000000..7f92c91386cc --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/package.json @@ -0,0 +1,69 @@ +{ + "name": "@stdlib/stats/base/dists/bradford/variance", + "version": "0.0.0", + "description": "Bradford distribution variance.", + "license": "Apache-2.0", + "author": { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + }, + "contributors": [ + { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + } + ], + "main": "./lib", + "directories": { + "benchmark": "./benchmark", + "doc": "./docs", + "example": "./examples", + "lib": "./lib", + "test": "./test" + }, + "types": "./docs/types", + "scripts": {}, + "homepage": "https://github.com/stdlib-js/stdlib", + "repository": { + "type": "git", + "url": "git://github.com/stdlib-js/stdlib.git" + }, + "bugs": { + "url": "https://github.com/stdlib-js/stdlib/issues" + }, + "dependencies": {}, + "devDependencies": {}, + "engines": { + "node": ">=0.10.0", + "npm": ">2.7.0" + }, + "os": [ + "aix", + "darwin", + "freebsd", + "linux", + "macos", + "openbsd", + "sunos", + "win32", + "windows" + ], + "keywords": [ + "stdlib", + "stdmath", + "statistics", + "stats", + "distribution", + "dist", + "bradford", + "bradford-distribution", + "parameter", + "shape-parameter", + "continuous", + "skewed", + "variance", + "dispersion", + "spread", + "univariate" + ] +} diff --git a/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/test/fixtures/python/large_c.json b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/test/fixtures/python/large_c.json new file mode 100644 index 000000000000..2ecf0954e561 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/test/fixtures/python/large_c.json @@ -0,0 +1 @@ +{"c": [1.0, 1.009009009009009, 1.018018018018018, 1.027027027027027, 1.0360360360360361, 1.045045045045045, 1.054054054054054, 1.063063063063063, 1.072072072072072, 1.0810810810810811, 1.09009009009009, 1.0990990990990992, 1.1081081081081081, 1.117117117117117, 1.1261261261261262, 1.135135135135135, 1.1441441441441442, 1.1531531531531531, 1.1621621621621623, 1.1711711711711712, 1.1801801801801801, 1.1891891891891893, 1.1981981981981982, 1.2072072072072073, 1.2162162162162162, 1.2252252252252251, 1.2342342342342343, 1.2432432432432432, 1.2522522522522523, 1.2612612612612613, 1.2702702702702702, 1.2792792792792793, 1.2882882882882882, 1.2972972972972974, 1.3063063063063063, 1.3153153153153152, 1.3243243243243243, 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you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +"""Generate fixtures.""" + +import os +import json +import numpy as np +from scipy.stats import bradford + +# Get the file path: +FILE = os.path.realpath(__file__) + +# Extract the directory in which this file resides: +DIR = os.path.dirname(FILE) + + +def gen(x, name): + """Generate fixture data and write to file. + + # Arguments + + * `x`: domain + * `name::str`: output filename + + # Examples + + ``` python + python> x = linspace(0.1, 100, 2001) + python> gen(x, './data.json') + ``` + """ + y = bradford.var(x) + + # Store data to be written to file as a dictionary: + data = { + "c": x.tolist(), + "expected": y.tolist() + } + + # Based on the script directory, create an output filepath: + filepath = os.path.join(DIR, name) + + # Write the data to the output filepath as JSON: + with open(filepath, "w", encoding="utf-8") as outfile: + json.dump(data, outfile) + + +def main(): + """Generate fixture data.""" + # Small shape parameter: + c = np.linspace(0.1, 1, 1000) + gen(c, "small_c.json") + + # Large shape parameter: + c = np.linspace(1, 10, 1000) + gen(c, "large_c.json") + + +if __name__ == "__main__": + main() diff --git a/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/test/fixtures/python/small_c.json b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/test/fixtures/python/small_c.json new file mode 100644 index 000000000000..57f3eb1033c2 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/bradford/variance/test/fixtures/python/small_c.json @@ 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License is distributed on an "AS IS" BASIS, +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +* See the License for the specific language governing permissions and +* limitations under the License. +*/ + +'use strict'; + +// MODULES // + +var tape = require( 'tape' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var NINF = require( '@stdlib/constants/float64/ninf' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var variance = require( './../lib' ); + + +// FIXTURES // + +var smallC = require( './fixtures/python/small_c.json' ); +var largeC = require( './fixtures/python/large_c.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof variance, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'if provided `NaN` for `c`, the function returns `NaN`', function test( t ) { + var v = variance( NaN ); + t.equal( isnan( v ), true, 'returns expected value' ); + t.end(); +}); + +tape( 'if provided `c <= 0`, the function returns `NaN`', function test( t ) { + var v; + + v = variance( 0.0 ); + t.equal( isnan( v ), true, 'returns expected value' ); + + v = variance( -1.0 ); + t.equal( isnan( v ), true, 'returns expected value' ); + + v = variance( NINF ); + t.equal( isnan( v ), true, 'returns expected value' ); + + t.end(); +}); + +tape( 'the function returns the variance of a Bradford distribution given small parameter `c`', function test( t ) { + var expected; + var delta; + var tol; + var i; + var c; + var y; + + expected = smallC.expected; + c = smallC.c; + for ( i = 0; i < expected.length; i++ ) { + y = variance( c[i] ); + if ( y === expected[i] ) { + t.equal( y, expected[i], 'c: '+c[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[ i ] ); + + /* + * NOTE: the tolerance is set high in this case due to: + * + * 1. The shape parameter being very small which causes differences in the `ln` calculations when compared to the test fixtures by SciPy. + * 2. The expected values being very small. + */ + tol = 643.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. c: '+c[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function returns the variance of a Bradford distribution given large parameter `c`', function test( t ) { + var expected; + var delta; + var tol; + var i; + var c; + var y; + + expected = largeC.expected; + c = largeC.c; + for ( i = 0; i < expected.length; i++ ) { + y = variance( c[i] ); + if ( y === expected[i] ) { + t.equal( y, expected[i], 'c: '+c[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 15.2 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. c: '+c[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +});