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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 pow = require( '@stdlib/math/base/special/pow' );
var ln = require( '@stdlib/math/base/special/ln' );
var log1p = require( '@stdlib/math/base/special/log1p' );
var NINF = require( '@stdlib/constants/float64/ninf' );
// MAIN //
/**
* Evaluates the natural logarithm of the cumulative distribution function (CDF) for a triangular distribution with lower limit `a` and upper limit `b` and mode `c` at a value `x`.
*
* @param {number} x - input value
* @param {number} a - lower limit
* @param {number} b - upper limit
* @param {number} c - mode
* @returns {number} evaluated logCDF
*
* @example
* var y = logcdf( 0.5, -1.0, 1.0, 0.0 );
* // returns ~-0.134
*
* @example
* var y = logcdf( 0.5, -1.0, 1.0, 0.5 );
* // returns ~-0.288
*
* @example
* var y = logcdf( -10.0, -20.0, 0.0, -2.0 );
* // returns ~-1.281
*
* @example
* var y = logcdf( -2.0, -1.0, 1.0, 0.0 );
* // returns -Infinity
*
* @example
* var y = logcdf( NaN, 0.0, 1.0, 0.5 );
* // returns NaN
*
* @example
* var y = logcdf( 0.0, NaN, 1.0, 0.5 );
* // returns NaN
*
* @example
* var y = logcdf( 0.0, 0.0, NaN, 0.5 );
* // returns NaN
*
* @example
* var y = logcdf( 2.0, 1.0, 0.0, NaN );
* // returns NaN
*
* @example
* var y = logcdf( 2.0, 1.0, 0.0, 1.5 );
* // returns NaN
*/
function logcdf( x, a, b, c ) {
var denom1;
var denom2;
if (
isnan( x ) ||
isnan( a ) ||
isnan( b ) ||
isnan( c ) ||
a > c ||
c > b
) {
return NaN;
}
if ( x <= a ) {
return NINF;
}
denom1 = ( b - a ) * ( c - a );
denom2 = ( b - a ) * ( b - c );
// Case: x > a
if ( x <= c ) {
return ( 2.0 * ln( x - a ) ) - ln( denom1 );
}
// Case: x > c
if ( x < b ) {
return log1p( -pow( b - x, 2.0 ) / denom2 );
}
// Case: x >= b
return 0.0;
}
// EXPORTS //
module.exports = logcdf;
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