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@stdlib/stats

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Standard library statistical functions.

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/** * @license Apache-2.0 * * Copyright (c) 2018 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' ); // MAIN // /** * Evaluates the probability density function (PDF) for a triangular distribution with lower limit `a` and upper limit `b` and mode `c` at a value `x`. * * @param {number} x - input value * @param {number} a - lower limit * @param {number} b - upper limit * @param {number} c - mode * @returns {number} evaluated PDF * * @example * var y = pdf( 0.5, -1.0, 1.0, 0.0 ); * // returns 0.5 * * @example * var y = pdf( 0.5, -1.0, 1.0, 0.5 ); * // returns 1.0 * * @example * var y = pdf( -10.0, -20.0, 0.0, -2.0 ); * // returns ~0.056 * * @example * var y = pdf( -2.0, -1.0, 1.0, 0.0 ); * // returns 0.0 * * @example * var y = pdf( NaN, 0.0, 1.0, 0.5 ); * // returns NaN * * @example * var y = pdf( 0.0, NaN, 1.0, 0.5 ); * // returns NaN * * @example * var y = pdf( 0.0, 0.0, NaN, 0.5 ); * // returns NaN * * @example * var y = pdf( 2.0, 1.0, 0.0, NaN ); * // returns NaN * * @example * var y = pdf( 2.0, 1.0, 0.0, 1.5 ); * // returns NaN */ function pdf( x, a, b, c ) { if ( isnan( x ) || isnan( a ) || isnan( b ) || isnan( c ) || a > c || c > b ) { return NaN; } if ( x < a ) { return 0.0; } // Case: x >= a if ( x < c ) { return ( 2.0 * ( x - a ) ) / ( ( b - a ) * ( c - a ) ); } if ( x === c ) { return 2.0 / ( b - a ); } // Case: x > c if ( x <= b ) { return ( 2.0 * ( b - x ) ) / ( ( b - a ) * ( b - c ) ); } // Case: x > b return 0.0; } // EXPORTS // module.exports = pdf;