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 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 | 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 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 3025x 3025x 3025x 3025x 3025x 3025x 3025x 3025x 3025x 3013x 3025x 17x 17x 3025x 4x 4x 3025x 4x 4x 3000x 3000x 3025x 527x 527x 527x 3025x 1218x 3025x 1255x 1255x 2473x 3025x 2473x 3025x 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 pow = require( '@stdlib/math/base/special/pow' );
var log1mexp = require( '@stdlib/math/base/special/log1mexp' );
var log1p = require( '@stdlib/math/base/special/log1p' );
var expm1 = require( '@stdlib/math/base/special/expm1' );
var ln = require( '@stdlib/math/base/special/ln' );
var NINF = require( '@stdlib/constants/float64/ninf' );
var FLOAT64_SMALLEST_NORMAL = require( '@stdlib/constants/float64/smallest-normal' );
// MAIN //
/**
* Evaluates the natural logarithm of the cumulative distribution function (CDF) for a Kumaraswamy's double bounded distribution with first shape parameter `a` and second shape parameter `b` at a value `x`.
*
* @param {number} x - input value
* @param {PositiveNumber} a - first shape parameter
* @param {PositiveNumber} b - second shape parameter
* @returns {number} evaluated logCDF
*
* @example
* var y = logcdf( 0.5, 1.0, 1.0 );
* // returns ~-0.693
*
* @example
* var y = logcdf( 0.5, 2.0, 4.0 );
* // returns ~-0.38
*
* @example
* var y = logcdf( 0.2, 2.0, 2.0 );
* // returns ~-2.546
*
* @example
* var y = logcdf( 0.8, 4.0, 4.0 );
* // returns ~-0.13
*
* @example
* var y = logcdf( -0.5, 4.0, 2.0 );
* // returns -Infinity
*
* @example
* var y = logcdf( 1.5, 4.0, 2.0 );
* // returns 0.0
*
* @example
* var y = logcdf( 2.0, -1.0, 0.5 );
* // returns NaN
*
* @example
* var y = logcdf( 2.0, 0.5, -1.0 );
* // returns NaN
*
* @example
* var y = logcdf( NaN, 1.0, 1.0 );
* // returns NaN
*
* @example
* var y = logcdf( 0.0, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = logcdf( 0.0, 1.0, NaN );
* // returns NaN
*/
function logcdf( x, a, b ) {
var u;
var v;
var t;
if (
isnan( x ) ||
isnan( a ) ||
isnan( b ) ||
a <= 0.0 ||
b <= 0.0
) {
return NaN;
}
if ( x <= 0.0 ) {
return NINF;
}
if ( x >= 1.0 ) {
return 0.0;
}
// Evaluate `v = ln(1-x^a)` without forming `1-x^a`, which rounds away the low-order bits of a small `x^a` and, for `x^a` close to `1`, of `1-x^a` itself:
u = pow( x, a );
if ( u < FLOAT64_SMALLEST_NORMAL ) {
// `x^a` is subnormal or underflows, so `ln(1-(1-x^a)^b) = ln(b) + a*ln(x)`:
return ln( b ) + ( a * ln( x ) );
}
if ( u < 0.5 ) {
v = log1p( -u );
} else {
v = ln( -expm1( a * ln( x ) ) );
}
t = b * v;
if ( t > -FLOAT64_SMALLEST_NORMAL ) {
return ln( b ) + ln( -v );
}
return log1mexp( t );
}
// EXPORTS //
module.exports = logcdf;
|