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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 asin = require( '@stdlib/math/base/special/asin' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var PI = require( '@stdlib/constants/float64/pi' );
// VARIABLES //
var TWO_OVER_PI = 2.0 / PI; // TODO: consider moving to pkg
// MAIN //
/**
* Evaluates the cumulative distribution function (CDF) for an arcsine distribution with minimum support `a` and maximum support `b` at a value `x`.
*
* @param {number} x - input value
* @param {number} a - minimum support
* @param {number} b - maximum support
* @returns {Probability} evaluated CDF
*
* @example
* var y = cdf( 9.0, 0.0, 10.0 );
* // returns ~0.795
*
* @example
* var y = cdf( 0.5, 0.0, 2.0 );
* // returns ~0.333
*
* @example
* var y = cdf( +Infinity, 2.0, 4.0 );
* // returns 1.0
*
* @example
* var y = cdf( -Infinity, 2.0, 4.0 );
* // returns 0.0
*
* @example
* var y = cdf( NaN, 0.0, 1.0 );
* // returns NaN
*
* @example
* var y = cdf( 0.0, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = cdf( 0.0, 0.0, NaN );
* // returns NaN
*
* @example
* var y = cdf( 2.0, 1.0, 0.0 );
* // returns NaN
*/
function cdf( x, a, b ) {
if (
isnan( x ) ||
isnan( a ) ||
isnan( b ) ||
a >= b
) {
return NaN;
}
if ( x < a ) {
return 0.0;
}
if ( x >= b ) {
return 1.0;
}
return TWO_OVER_PI * asin( sqrt( ( x-a ) / ( b-a ) ) );
}
// EXPORTS //
module.exports = cdf;
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