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 | 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 4013x 4013x 4013x 4013x 4008x 4013x 10x 10x 4003x 4003x 4003x 4003x 4003x 4003x 4003x 4003x 4003x 4003x 4003x 4003x 4003x 4003x 4003x 3x 3x 4000x 4003x 1255x 1255x 4003x 1284x 1284x 1461x 4003x 4013x 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 tan = require( '@stdlib/math/base/special/tan' );
var PI = require( '@stdlib/constants/float64/pi' );
// MAIN //
/**
* Returns a function for evaluating the quantile function for a Cauchy distribution with location parameter `x0` and scale parameter `gamma`.
*
* @param {number} x0 - location parameter
* @param {PositiveNumber} gamma - scale parameter
* @returns {Function} quantile function
*
* @example
* var quantile = factory( 10.0, 2.0 );
* var y = quantile( 0.2 );
* // returns ~7.247
*
* y = quantile( 0.8 );
* // returns ~12.753
*/
function factory( x0, gamma ) {
if (
isnan( x0 ) ||
isnan( gamma ) ||
gamma <= 0.0
) {
return constantFunction( NaN );
}
return quantile;
/**
* Evaluates the quantile function for a Cauchy distribution.
*
* @private
* @param {Probability} p - input value
* @returns {number} evaluated quantile function
*
* @example
* var y = quantile( 0.3 );
* // returns <number>
*/
function quantile( p ) {
if ( isnan( p ) || p < 0.0 || p > 1.0 ) {
return NaN;
}
// `p-0.5` rounds away the low-order bits of a `p` close to `0` (`tan(PI*(p-0.5)) = -1/tan(PI*p)`), so evaluate each tail from its own probability, which is exact (`1-p` for `p > 0.75`):
if ( p < 0.25 ) {
return x0 - ( gamma / tan( PI*p ) );
}
if ( p > 0.75 ) {
return x0 + ( gamma / tan( PI*( 1.0-p ) ) );
}
return x0 + ( gamma * tan( PI*( p-0.5 ) ) );
}
}
// EXPORTS //
module.exports = factory;
|