time-to-botec

Benchmark sampling in different programming languages
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logcdf.js (1876B)

      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 atan2 = require( '@stdlib/math/base/special/atan2' );
     25 var ln = require( '@stdlib/math/base/special/ln' );
     26 
     27 
     28 // VARIABLES //
     29 
     30 var ONE_OVER_PI = 0.3183098861837907;
     31 
     32 
     33 // MAIN //
     34 
     35 /**
     36 * Evaluates the natural logarithm of the cumulative distribution function (logCDF) for a Cauchy distribution with location parameter `x0` and scale parameter `gamma` at a value `x`.
     37 *
     38 * @param {number} x - input value
     39 * @param {number} x0 - location parameter
     40 * @param {PositiveNumber} gamma - scale parameter
     41 * @returns {number} evaluated logCDF
     42 *
     43 * @example
     44 * var y = logcdf( 4.0, 0.0, 2.0 );
     45 * // returns ~-0.16
     46 *
     47 * @example
     48 * var y = logcdf( 1.0, 0.0, 2.0 );
     49 * // returns ~-0.435
     50 *
     51 * @example
     52 * var y = logcdf( 1.0, 3.0, 2.0 );
     53 * // returns ~-1.386
     54 *
     55 * @example
     56 * var y = logcdf( NaN, 0.0, 2.0 );
     57 * // returns NaN
     58 *
     59 * @example
     60 * var y = logcdf( 1.0, 2.0, NaN );
     61 * // returns NaN
     62 *
     63 * @example
     64 * var y = logcdf( 1.0, NaN, 3.0 );
     65 * // returns NaN
     66 */
     67 function logcdf( x, x0, gamma ) {
     68 	if (
     69 		isnan( x ) ||
     70 		isnan( gamma ) ||
     71 		isnan( x0 ) ||
     72 		gamma <= 0.0
     73 	) {
     74 		return NaN;
     75 	}
     76 	return ln( ( ONE_OVER_PI * atan2( x-x0, gamma ) ) + 0.5 );
     77 }
     78 
     79 
     80 // EXPORTS //
     81 
     82 module.exports = logcdf;