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* @license Apache-2.0
*
* Copyright (c) 2026 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 log1p = require( '@stdlib/math/base/special/log1p' );
var ln = require( '@stdlib/math/base/special/ln' );
var pow = require( '@stdlib/math/base/special/pow' );
var NINF = require( '@stdlib/constants/float64/ninf' );
// MAIN //
/**
* Evaluates the natural logarithm of the cumulative distribution function (CDF) for a log-logistic distribution with scale parameter `alpha` and shape parameter `beta` at a value `x`.
*
* @param {number} x - input value
* @param {PositiveNumber} alpha - scale parameter
* @param {PositiveNumber} beta - shape parameter
* @returns {number} evaluated logCDF
*
* @example
* var y = logcdf( 2.0, 1.0, 1.0 );
* // returns ~-0.405
*
* @example
* var y = logcdf( 4.0, 2.0, 3.0 );
* // returns ~-0.118
*
* @example
* var y = logcdf( -1.0, 1.0, 1.0 );
* // returns -Infinity
*
* @example
* var y = logcdf( 0.0, 1.0, 1.0 );
* // returns -Infinity
*
* @example
* var y = logcdf( NaN, 1.0, 1.0 );
* // returns NaN
*
* @example
* var y = logcdf( 1.0, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = logcdf( 1.0, 1.0, NaN );
* // returns NaN
*
* @example
* var y = logcdf( 1.0, -1.0, 1.0 );
* // returns NaN
*
* @example
* var y = logcdf( 1.0, 1.0, -1.0 );
* // returns NaN
*/
function logcdf( x, alpha, beta ) {
var base;
var xb;
if (
isnan( x ) ||
isnan( alpha ) ||
isnan( beta ) ||
alpha <= 0.0 ||
beta <= 0.0
) {
return NaN;
}
if ( x <= 0.0 ) {
return NINF;
}
// Select the algebraically equivalent form which keeps the intermediate power bounded, thus avoiding overflow to infinity as `x` grows large, while preserving accuracy in the lower tail...
if ( x <= alpha ) {
base = x / alpha;
xb = pow( base, beta );
return ( beta * ln( base ) ) - log1p( xb );
}
return -log1p( pow( alpha / x, beta ) );
}
// EXPORTS //
module.exports = logcdf;
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