Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 | 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 4012x 4012x 4012x 4012x 4012x 4008x 4012x 10x 10x 4002x 4012x 3001x 3001x 1001x 4012x 13x 13x 988x 4012x 2x 2x 2x 2x 2x | /**
* @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' );
var atan2 = require( '@stdlib/math/base/special/atan2' );
var ln = require( '@stdlib/math/base/special/ln' );
var log1p = require( '@stdlib/math/base/special/log1p' );
// VARIABLES //
var ONE_OVER_PI = 0.3183098861837907;
// MAIN //
/**
* 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`.
*
* @param {number} x - input value
* @param {number} x0 - location parameter
* @param {PositiveNumber} gamma - scale parameter
* @returns {number} evaluated logCDF
*
* @example
* var y = logcdf( 4.0, 0.0, 2.0 );
* // returns ~-0.16
*
* @example
* var y = logcdf( 1.0, 0.0, 2.0 );
* // returns ~-0.435
*
* @example
* var y = logcdf( 1.0, 3.0, 2.0 );
* // returns ~-1.386
*
* @example
* var y = logcdf( NaN, 0.0, 2.0 );
* // returns NaN
*
* @example
* var y = logcdf( 1.0, 2.0, NaN );
* // returns NaN
*
* @example
* var y = logcdf( 1.0, NaN, 3.0 );
* // returns NaN
*/
function logcdf( x, x0, gamma ) {
if (
isnan( x ) ||
isnan( x0 ) ||
isnan( gamma ) ||
gamma <= 0.0
) {
return NaN;
}
// Below `z = -1`, `0.5 + atan(z)/pi` cancels more and more as `z` goes to `-infinity`; `atan2( gamma, x0-x )/pi` is the same quantity evaluated without the subtraction. Nearer the median the sum does not cancel and is the more accurate of the two...
if ( x-x0 < -gamma ) {
return ln( ONE_OVER_PI * atan2( gamma, x0-x ) );
}
// Above `z = 1`, the result is `ln` of a number approaching `1`, so evaluate `ln(1 - atan2(gamma, x-x0)/pi)` with `log1p` instead...
if ( x-x0 > gamma ) {
return log1p( -ONE_OVER_PI * atan2( gamma, x-x0 ) );
}
return ln( ( ONE_OVER_PI * atan2( x-x0, gamma ) ) + 0.5 );
}
// EXPORTS //
module.exports = logcdf;
|