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 93 94 | 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 4014x 4014x 4014x 4014x 4009x 4014x 10x 10x 4004x 4004x 4004x 4004x 4004x 4004x 4004x 4004x 4004x 4004x 4004x 4004x 4004x 4004x 4003x 1x 1x 4002x 4003x 3001x 3001x 1001x 4003x 13x 13x 988x 4003x 4014x 3x 3x 3x 3x 3x | /**
* @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 constantFunction = require( '@stdlib/utils/constant-function' );
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 //
/**
* Returns a function for evaluating the natural logarithm of the cumulative distribution function (logCDF) for a Cauchy distribution with location parameter `x0` and scale parameter `gamma`.
*
* @param {number} x0 - location parameter
* @param {PositiveNumber} gamma - scale parameter
* @returns {Function} logCDF
*
* @example
* var logcdf = factory( 10.0, 2.0 );
*
* var y = logcdf( 10.0 );
* // returns ~-0.693
*
* y = logcdf( 12.0 );
* // returns ~-0.288
*/
function factory( x0, gamma ) {
if (
isnan( x0 ) ||
isnan( gamma ) ||
gamma <= 0.0
) {
return constantFunction( NaN );
}
return logcdf;
/**
* Evaluates the natural logarithm of the cumulative distribution function (logCDF) for a Cauchy distribution.
*
* @private
* @param {number} x - input value
* @returns {number} evaluated logCDF
*
* @example
* var y = logcdf( 2.0 );
* // returns <number>
*/
function logcdf( x ) {
if ( isnan( x ) ) {
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 = factory;
|