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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' );
// MAIN //
/**
* Evaluates 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 {Probability} evaluated CDF
*
* @example
* var y = cdf( 0.5, -1.0, 1.0, 0.0 );
* // returns 0.875
*
* @example
* var y = cdf( 0.5, -1.0, 1.0, 0.5 );
* // returns 0.75
*
* @example
* var y = cdf( -10.0, -20.0, 0.0, -2.0 );
* // returns ~0.278
*
* @example
* var y = cdf( -2.0, -1.0, 1.0, 0.0 );
* // returns 0.0
*
* @example
* var y = cdf( NaN, 0.0, 1.0, 0.5 );
* // returns NaN
*
* @example
* var y = cdf( 0.0, NaN, 1.0, 0.5 );
* // returns NaN
*
* @example
* var y = cdf( 0.0, 0.0, NaN, 0.5 );
* // returns NaN
*
* @example
* var y = cdf( 2.0, 1.0, 0.0, NaN );
* // returns NaN
*
* @example
* var y = cdf( 2.0, 1.0, 0.0, 1.5 );
* // returns NaN
*/
function cdf( 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 0.0;
}
denom1 = ( b - a ) * ( c - a );
denom2 = ( b - a ) * ( b - c );
// Case: x > a
if ( x <= c ) {
return pow( x - a, 2.0 ) / denom1;
}
// Case: x > c
if ( x < b ) {
return 1.0 - ( pow( b - x, 2.0 ) / denom2 );
}
// Case: x >= b
return 1.0;
}
// EXPORTS //
module.exports = cdf;
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