diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/README.md b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/README.md new file mode 100644 index 000000000000..a4f1d5a8ba0e --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/README.md @@ -0,0 +1,139 @@ + + +# Kurtosis + +> Planck (discrete exponential) distribution [excess kurtosis][kurtosis]. + + + +
+ +The [excess kurtosis][kurtosis] for a Planck random variable is + + + +```math +\mathop{\mathrm{Kurt}}\left( X \right) = 4 + 2 \cosh(\lambda) +``` + + + +where `λ` is the shape parameter. + +
+ + + + + +
+ +## Usage + +```javascript +var kurtosis = require( '@stdlib/stats/base/dists/planck/kurtosis' ); +``` + +#### kurtosis( lambda ) + +Returns the [excess kurtosis][kurtosis] of a Planck distribution with shape parameter `lambda`. + +```javascript +var v = kurtosis( 0.1 ); +// returns ~6.0100 + +v = kurtosis( 1.5 ); +// returns ~8.7048 +``` + +If provided a shape parameter `lambda` which is nonpositive or `NaN`, the function returns `NaN`. + +```javascript +var v = kurtosis( NaN ); +// returns NaN + +v = kurtosis( -1.5 ); +// returns NaN +``` + +
+ + + + + +
+ +
+ + + + + +
+ +## Examples + + + +```javascript +var uniform = require( '@stdlib/random/array/uniform' ); +var kurtosis = require( '@stdlib/stats/base/dists/planck/kurtosis' ); + +var lambda = uniform( 10, 0.1, 10.0 ); + +var v; +var i; +for ( i = 0; i < lambda.length; i++ ) { + v = kurtosis( lambda[ i ] ); + console.log( 'λ: %d, Kurt(X;λ): %d', lambda[ i ].toFixed( 4 ), v.toFixed( 4 ) ); +} +``` + +
+ + + + + +
+ +
+ + + + + +
+ +
+ + + + + +
+ +[kurtosis]: https://en.wikipedia.org/wiki/Kurtosis + +
+ + diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/benchmark/benchmark.js new file mode 100644 index 000000000000..2ed19485a1b2 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/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 kurtosis = require( './../lib' ); + + +// MAIN // + +bench( pkg, function benchmark( b ) { + var lambda; + var y; + var i; + + lambda = uniform( 100, 0.1, 10.0 ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + y = kurtosis( lambda[ i % lambda.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/planck/kurtosis/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/docs/repl.txt new file mode 100644 index 000000000000..7f8d80a1e293 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/docs/repl.txt @@ -0,0 +1,27 @@ + +{{alias}}( λ ) + Returns the excess kurtosis of a Planck distribution with shape parameter + `λ`. + + If `λ <= 0`, the function returns `NaN`. + + Parameters + ---------- + λ: number + Shape parameter. + + Returns + ------- + out: number + Excess kurtosis. + + Examples + -------- + > var v = {{alias}}( 0.1 ) + ~6.0100 + > v = {{alias}}( 1.5 ) + ~8.7048 + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/docs/types/index.d.ts new file mode 100644 index 000000000000..1de97e2f3119 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/docs/types/index.d.ts @@ -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. +*/ + +// TypeScript Version: 4.1 + +/** +* Returns the excess kurtosis of a Planck distribution. +* +* ## Notes +* +* - If `lambda <= 0`, the function returns `NaN`. +* +* @param lambda - shape parameter +* @returns kurtosis +* +* @example +* var v = kurtosis( 0.1 ); +* // returns ~6.0100 +* +* @example +* var v = kurtosis( 1.5 ); +* // returns ~8.7048 +* +* @example +* var v = kurtosis( -1.1 ); +* // returns NaN +* +* @example +* var v = kurtosis( NaN ); +* // returns NaN +*/ +declare function kurtosis( lambda: number ): number; + + +// EXPORTS // + +export = kurtosis; diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/docs/types/test.ts b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/docs/types/test.ts new file mode 100644 index 000000000000..32f723300471 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/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 kurtosis = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + kurtosis( 0.3 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided a value other than a number... +{ + kurtosis( true ); // $ExpectError + kurtosis( false ); // $ExpectError + kurtosis( null ); // $ExpectError + kurtosis( undefined ); // $ExpectError + kurtosis( '5' ); // $ExpectError + kurtosis( [] ); // $ExpectError + kurtosis( {} ); // $ExpectError + kurtosis( ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided insufficient arguments... +{ + kurtosis(); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/examples/index.js b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/examples/index.js new file mode 100644 index 000000000000..13f77f695509 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/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 kurtosis = require( './../lib' ); + +var lambda = uniform( 10, 0.1, 10.0 ); + +var v; +var i; +for ( i = 0; i < lambda.length; i++ ) { + v = kurtosis( lambda[ i ] ); + console.log( 'λ: %d, Kurt(X;λ): %d', lambda[ i ].toFixed( 4 ), v.toFixed( 4 ) ); +} diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/lib/index.js b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/lib/index.js new file mode 100644 index 000000000000..082da5dc4278 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/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'; + +/** +* Planck distribution excess kurtosis. +* +* @module @stdlib/stats/base/dists/planck/kurtosis +* +* @example +* var kurtosis = require( '@stdlib/stats/base/dists/planck/kurtosis' ); +* +* var v = kurtosis( 0.1 ); +* // returns ~6.0100 +* +* v = kurtosis( 1.5 ); +* // returns ~8.7048 +*/ + +// MODULES // + +var main = require( './main.js' ); + + +// EXPORTS // + +module.exports = main; diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/lib/main.js new file mode 100644 index 000000000000..29fadca2ac42 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/lib/main.js @@ -0,0 +1,61 @@ +/** +* @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 cosh = require( '@stdlib/math/base/special/cosh' ); + + +// MAIN // + +/** +* Returns the excess kurtosis of a Planck distribution. +* +* @param {PositiveNumber} lambda - shape parameter +* @returns {PositiveNumber} kurtosis +* +* @example +* var v = kurtosis( 0.1 ); +* // returns ~6.0100 +* +* @example +* var v = kurtosis( 1.5 ); +* // returns ~8.7048 +* +* @example +* var v = kurtosis( -1.1 ); +* // returns NaN +* +* @example +* var v = kurtosis( NaN ); +* // returns NaN +*/ +function kurtosis( lambda ) { + if ( isnan( lambda ) || lambda <= 0.0 ) { + return NaN; + } + return 4.0 + ( 2.0 * cosh( lambda ) ); +} + + +// EXPORTS // + +module.exports = kurtosis; diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/package.json b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/package.json new file mode 100644 index 000000000000..89011730cb52 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/package.json @@ -0,0 +1,68 @@ +{ + "name": "@stdlib/stats/base/dists/planck/kurtosis", + "version": "0.0.0", + "description": "Planck (discrete exponential) distribution excess kurtosis.", + "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", + "parameter", + "memoryless", + "life-time", + "discrete", + "kurtosis", + "excess", + "tails", + "planck", + "univariate" + ] +} diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/test/fixtures/python/data.json b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/test/fixtures/python/data.json new file mode 100644 index 000000000000..e36ad295a2d2 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/test/fixtures/python/data.json @@ -0,0 +1 @@ +{"lambda": [4.975162669672901, 9.489932723747437, 9.147662763199428, 7.485806747136657, 11.453311635593124, 2.7572468600606115, 4.772164918540753, 18.427039841658434, 11.513514163377618, 3.4056518060090846, 10.496093119695294, 16.643555884495335, 10.387625296849157, 19.90659095126921, 14.436653079797866, 16.38618293037597, 0.6486005946342499, 15.17021139359711, 13.510306621439266, 17.931878813902628, 6.958456296603708, 5.636833791613681, 5.129235681164392, 18.851644559724484, 1.5145862189290438, 8.510293534534025, 11.941231890434496, 17.39976633926515, 6.065343452976366, 16.4488911177914, 19.921514031349187, 3.2945985164072744, 15.092177459239144, 9.65680851192754, 5.835184505225451, 17.396776375159604, 18.279650119912418, 4.329048528572876, 2.762393713394231, 9.300356783902963, 9.904484720762117, 14.992197917585523, 16.031817737877766, 6.060163356431412, 15.626650266055167, 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2286677.6720682927, 8.732000495988185, 243.26384680906162, 211511807.33906865, 5829.073188617783, 471890.37915724504, 12478447.514436219, 877.8497858628253, 7420.601575188877, 354.11547686629433, 3970252.284547869, 247716296.2347697, 55354.437520415195, 1570429.1748452946, 12139399.912856596, 70.39178640964268, 6.939881835655007, 86793400.96257105]} diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/test/fixtures/python/runner.py b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/test/fixtures/python/runner.py new file mode 100644 index 000000000000..161e06609ee9 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/test/fixtures/python/runner.py @@ -0,0 +1,77 @@ +#!/usr/bin/env python +# +# @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. + +"""Generate fixtures.""" + +import os +import json +import numpy as np +from scipy.stats import planck + +# Get the file path: +FILE = os.path.realpath(__file__) + +# Extract the directory in which this file resides: +DIR = os.path.dirname(FILE) + + +def gen(lam, name): + """ + Generate fixture data and write to file. + + # Arguments + + * `lam`: shape parameter. + * `name::str`: output filename. + + # Examples + + ```python + python> lam = np.random.rand(1000) * 20 + python> gen(lam, "data.json") + ``` + """ + # Compute excess kurtosis values: + z = np.array(planck.stats(lam, moments='k')) + + # Store data to be written to file as a dictionary: + data = { + "lambda": lam.tolist(), + "expected": z.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) + + # Include trailing newline: + with open(filepath, "a", encoding='utf-8') as outfile: + outfile.write("\n") + + +def main(): + """Generate fixture data.""" + lam = np.random.rand(1000) * 20.0 + gen(lam, "data.json") + + +if __name__ == "__main__": + main() diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/test/test.js b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/test/test.js new file mode 100644 index 000000000000..e6fa6f90296f --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/planck/kurtosis/test/test.js @@ -0,0 +1,82 @@ +/** +* @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 tape = require( 'tape' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var kurtosis = require( './../lib' ); + + +// FIXTURES // + +var data = require( './fixtures/python/data.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof kurtosis, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'if provided `NaN` for `lambda`, the function returns `NaN`', function test( t ) { + var v = kurtosis( NaN ); + t.equal( isnan( v ), true, 'returns NaN' ); + t.end(); +}); + +tape( 'if provided a shape parameter `lambda` which is nonpositive, the function returns `NaN`', function test( t ) { + var v; + + v = kurtosis( 0.0 ); + t.equal( isnan( v ), true, 'returns NaN' ); + + v = kurtosis( -1.5 ); + t.equal( isnan( v ), true, 'returns NaN' ); + + t.end(); +}); + +tape( 'the function returns the excess kurtosis of a Planck distribution', function test( t ) { + var expected; + var lambda; + var delta; + var tol; + var i; + var y; + + expected = data.expected; + lambda = data.lambda; + for ( i = 0; i < expected.length; i++ ) { + y = kurtosis( lambda[ i ] ); + if ( y === expected[ i ] ) { + t.equal( y, expected[ i ], 'lambda: '+lambda[ i ]+', y: '+y+', expected: '+expected[ i ] ); + } else { + delta = abs( y - expected[ i ] ); + tol = 1.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. lambda: '+lambda[ i ]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +});