@stdlib/stats/base/dists/normal/logcdf/lib/main.js

Standard library statistical functions.

/**
* @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;