time-to-botec

Benchmark sampling in different programming languages
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cdf.js (1883B)

      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 betainc = require( '@stdlib/math/base/special/betainc' );
     24 var isnan = require( '@stdlib/math/base/assert/is-nan' );
     25 var pow = require( '@stdlib/math/base/special/pow' );
     26 
     27 
     28 // MAIN //
     29 
     30 /**
     31 * Evaluates the cumulative distribution function (CDF) for a Student's t distribution with degrees of freedom `v` at a value `x`.
     32 *
     33 * @param {number} x - input value
     34 * @param {PositiveNumber} v - degrees of freedom
     35 * @returns {Probability} evaluated CDF
     36 *
     37 * @example
     38 * var y = cdf( 2.0, 0.1 );
     39 * // returns ~0.611
     40 *
     41 * @example
     42 * var y = cdf( 1.0, 2.0 );
     43 * // returns ~0.789
     44 *
     45 * @example
     46 * var y = cdf( -1.0, 4.0 );
     47 * // returns ~0.187
     48 *
     49 * @example
     50 * var y = cdf( NaN, 1.0 );
     51 * // returns NaN
     52 *
     53 * @example
     54 * var y = cdf( 0.0, NaN );
     55 * // returns NaN
     56 *
     57 * @example
     58 * var y = cdf( 2.0, -1.0 );
     59 * // returns NaN
     60 */
     61 function cdf( x, v ) {
     62 	var x2;
     63 	var p;
     64 	var z;
     65 	if (
     66 		isnan( x ) ||
     67 		isnan( v ) ||
     68 		v <= 0.0
     69 	) {
     70 		return NaN;
     71 	}
     72 	if ( x === 0.0 ) {
     73 		return 0.5;
     74 	}
     75 	x2 = pow( x, 2.0 );
     76 	if ( v > 2.0*x2 ) {
     77 		z = x2 / ( v + x2 );
     78 		p = betainc( z, 0.5, v/2.0, true, true ) / 2.0;
     79 	} else {
     80 		z = v / ( v + x2 );
     81 		p = betainc( z, v/2.0, 0.5, true, false ) / 2.0;
     82 	}
     83 	return ( x > 0.0 ) ? 1.0 - p : p;
     84 }
     85 
     86 
     87 // EXPORTS //
     88 
     89 module.exports = cdf;