time-to-botec

Benchmark sampling in different programming languages
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pdf.js (2353B)

      1 /**
      2 * @license Apache-2.0
      3 *
      4 * Copyright (c) 2018 The Stdlib Authors.
      5 *
      6 * Licensed under the Apache License, Version 2.0 (the "License");
      7 * you may not use this file except in compliance with the License.
      8 * You may obtain a copy of the License at
      9 *
     10 *    http://www.apache.org/licenses/LICENSE-2.0
     11 *
     12 * Unless required by applicable law or agreed to in writing, software
     13 * distributed under the License is distributed on an "AS IS" BASIS,
     14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     15 * See the License for the specific language governing permissions and
     16 * limitations under the License.
     17 */
     18 
     19 'use strict';
     20 
     21 // MODULES //
     22 
     23 var isnan = require( '@stdlib/math/base/assert/is-nan' );
     24 var PINF = require( '@stdlib/constants/float64/pinf' );
     25 var ibetaDerivative = require( './ibeta_derivative.js' );
     26 
     27 
     28 // MAIN //
     29 
     30 /**
     31 * Evaluates the probability density function (PDF) for an F distribution with numerator degrees of freedom `d1` and denominator degrees of freedom `d2` at a value `x`.
     32 *
     33 * @param {number} x - input value
     34 * @param {PositiveNumber} d1 - numerator degrees of freedom
     35 * @param {PositiveNumber} d2 - denominator degrees of freedom
     36 * @returns {number} evaluated PDF
     37 *
     38 * @example
     39 * var y = pdf( 2.0, 0.5, 1.0 );
     40 * // returns ~0.057
     41 *
     42 * @example
     43 * var y = pdf( 0.1, 1.0, 1.0 );
     44 * // returns ~0.915
     45 *
     46 * @example
     47 * var y = pdf( -1.0, 4.0, 2.0 );
     48 * // returns 0.0
     49 *
     50 * @example
     51 * var y = pdf( NaN, 1.0, 1.0 );
     52 * // returns NaN
     53 *
     54 * @example
     55 * var y = pdf( 0.0, NaN, 1.0 );
     56 * // returns NaN
     57 *
     58 * @example
     59 * var y = pdf( 0.0, 1.0, NaN );
     60 * // returns NaN
     61 *
     62 * @example
     63 * var y = pdf( 2.0, 1.0, -1.0 );
     64 * // returns NaN
     65 *
     66 * @example
     67 * var y = pdf( 2.0, -1.0, 1.0 );
     68 * // returns NaN
     69 */
     70 function pdf( x, d1, d2 ) {
     71 	var v1x;
     72 	var y;
     73 	var z;
     74 	if (
     75 		isnan( x ) ||
     76 		isnan( d1 ) ||
     77 		isnan( d2 ) ||
     78 		d1 <= 0.0 ||
     79 		d2 <= 0.0
     80 	) {
     81 		return NaN;
     82 	}
     83 	if ( x < 0.0 || x === PINF ) {
     84 		return 0.0;
     85 	}
     86 	if ( x === 0.0 ) {
     87 		if ( d1 < 2.0 ) {
     88 			return PINF;
     89 		}
     90 		if ( d1 === 2.0 ) {
     91 			return 1.0;
     92 		}
     93 		return 0.0;
     94 	}
     95 	v1x = d1 * x;
     96 	if ( v1x > d2 ) {
     97 		y = ( d2 * d1 ) / ( ( d2 + v1x ) * ( d2 + v1x ) );
     98 		return y * ibetaDerivative( d2 / ( d2+v1x ), d2/2.0, d1/2.0 );
     99 	}
    100 	z = d2 + v1x;
    101 	y = ((z * d1) - (x * d1 * d1)) / ( z * z );
    102 	return y * ibetaDerivative( v1x / ( d2+v1x ), d1/2.0, d2/2.0 );
    103 }
    104 
    105 
    106 // EXPORTS //
    107 
    108 module.exports = pdf;