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 | 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x | /**
* @license Apache-2.0
*
* Copyright (c) 2022 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 ln = require( '@stdlib/math/base/special/ln' );
var log1p = require( '@stdlib/math/base/special/log1p' );
var abs2 = require( '@stdlib/math/base/special/abs2' );
var erfc = require( '@stdlib/math/base/special/erfc' );
var erfcx = require( '@stdlib/math/base/special/erfcx' );
var NINF = require( '@stdlib/constants/float64/ninf' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
// VARIABLES //
var INV_SQRT_TWO = 0.7071067811865475; // 1/sqrt(2)
// MAIN //
/**
* Evaluates the natural logarithm of the cumulative distribution function (CDF) for a normal distribution with mean `mu` and standard deviation `sigma` at a value `x`.
*
* @param {number} x - input value
* @param {number} mu - mean
* @param {NonNegativeNumber} sigma - standard deviation
* @returns {number} logarithm of cumulative distribution function
*
* @example
* var y = logcdf( 2.0, 0.0, 1.0 );
* // returns ~-0.023
*
* @example
* var y = logcdf( -1.0, 4.0, 2.0 );
* // returns ~-5.082
*
* @example
* var y = logcdf( NaN, 0.0, 1.0 );
* // returns NaN
*
* @example
* var y = logcdf( 0.0, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = logcdf( 0.0, 0.0, NaN );
* // returns NaN
*
* @example
* // Negative standard deviation:
* var y = logcdf( 2.0, 0.0, -1.0 );
* // returns NaN
*
* @example
* var y = logcdf( 2.0, 8.0, 0.0 );
* // returns -Infinity
*
* @example
* var y = logcdf( 8.0, 8.0, 0.0 );
* // returns 0.0
*/
function logcdf( x, mu, sigma ) {
var z;
if (
isnan( x ) ||
isnan( mu ) ||
isnan( sigma ) ||
sigma < 0.0
) {
return NaN;
}
if ( sigma === 0.0 ) {
return (x < mu) ? NINF : 0.0;
}
z = ( x - mu ) / sigma;
if ( z < -1.0 ) {
return ln( erfcx( -z * INV_SQRT_TWO ) / 2.0 ) - ( abs2(z) / 2.0 );
}
// Case: z >= -1.0:
return log1p( -erfc( z * INV_SQRT_TWO ) / 2.0 );
}
// EXPORTS //
module.exports = logcdf;
|