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* @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 erfc = require( '@stdlib/math/base/special/erfc' );
var erfcx = require( '@stdlib/math/base/special/erfcx' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var NINF = require( '@stdlib/constants/float64/ninf' );
var ln = require( '@stdlib/math/base/special/ln' );
// MAIN //
/**
* Evaluates the natural logarithm of the cumulative distribution function (CDF) for a Lévy distribution with location parameter `mu` and scale parameter `c` at value `x`.
*
* @param {number} x - input value
* @param {number} mu - location parameter
* @param {PositiveNumber} c - scale parameter
* @returns {number} evaluated logCDF
*
* @example
* var y = logcdf( 2.0, 0.0, 1.0 );
* // returns ~-0.735
*
* @example
* var y = logcdf( 12.0, 10.0, 3.0 );
* // returns ~-1.51
*
* @example
* var y = logcdf( 9.0, 10.0, 3.0 );
* // returns -Infinity
*
* @example
* var y = logcdf( NaN, 0.0, 1.0 );
* // returns NaN
*
* @example
* var y = logcdf( 2, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = logcdf( 2.0, 0.0, NaN );
* // returns NaN
*
* @example
* // Negative scale parameter:
* var y = logcdf( 2.0, 0.0, -1.0 );
* // returns NaN
*/
function logcdf( x, mu, c ) {
var w;
var z;
if (
isnan( x ) ||
isnan( mu ) ||
isnan( c ) ||
c <= 0.0
) {
return NaN;
}
if ( x < mu ) {
return NINF;
}
w = c / ( 2.0 * ( x-mu ) );
z = sqrt( w );
if ( z < 1.0 ) {
return ln( erfc( z ) );
}
// `erfc(z)` underflows for `z > ~26.5`, so use `ln(erfc(z)) = ln(erfcx(z)) - z^2`:
return ln( erfcx( z ) ) - w;
}
// EXPORTS //
module.exports = logcdf;
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