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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 ln = require( '@stdlib/math/base/special/ln' );
var LN_PI = require( '@stdlib/constants/float64/ln-pi' );
var NINF = require( '@stdlib/constants/float64/ninf' );
// MAIN //
/**
* Evaluates the logarithm of the probability density function (PDF) 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 {number} evaluated logPDF
*
* @example
* var y = logpdf( 2.0, 0.0, 4.0 );
* // returns ~-1.838
*
* @example
* var y = logpdf( 5.0, 0.0, 4.0 );
* // returns -Infinity
*
* @example
* var y = logpdf( 0.25, 0.0, 1.0 );
* // returns ~-0.308
*
* @example
* var y = logpdf( NaN, 0.0, 1.0 );
* // returns NaN
*
* @example
* var y = logpdf( 0.0, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = logpdf( 0.0, 0.0, NaN );
* // returns NaN
*
* @example
* var y = logpdf( 2.0, 3.0, 1.0 );
* // returns NaN
*/
function logpdf( x, a, b ) {
if (
isnan( x ) ||
isnan( a ) ||
isnan( b ) ||
a >= b
) {
return NaN;
}
if ( x < a || x > b ) {
return NINF;
}
return -( LN_PI + ( ln( ( x-a ) * ( b-x ) ) / 2.0 ) );
}
// EXPORTS //
module.exports = logpdf;
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