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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 constantFunction = require( '@stdlib/utils/constant-function' );
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;
// MAIN //
/**
* Returns a function for evaluating the cumulative distribution function (CDF) for an arcsine distribution with minimum support `a` and maximum support `b`.
*
* @param {number} a - minimum support
* @param {number} b - maximum support
* @returns {Function} CDF
*
* @example
* var cdf = factory( 0.0, 10.0 );
* var y = cdf( 0.5 );
* // returns ~0.144
*
* y = cdf( 8.0 );
* // returns ~0.705
*/
function factory( a, b ) {
if (
isnan( a ) ||
isnan( b ) ||
a >= b
) {
return constantFunction( NaN );
}
return cdf;
/**
* Evaluates the cumulative distribution function (CDF) for an arcsine distribution.
*
* @private
* @param {number} x - input value
* @returns {Probability} evaluated CDF
*
* @example
* var y = cdf( 2.0 );
* // returns <number>
*/
function cdf( x ) {
if ( isnan( x ) ) {
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 = factory;
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