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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 PINF = require( '@stdlib/constants/float64/pinf' );
var NINF = require( '@stdlib/constants/float64/ninf' );
// MAIN //
/**
* Evaluates the natural logarithm of the probability density function (PDF) for a Kumaraswamy's double bounded distribution with first shape parameter `a` and second shape parameter `b` at a value `x`.
*
* @param {number} x - input value
* @param {PositiveNumber} a - first shape parameter
* @param {PositiveNumber} b - second shape parameter
* @returns {number} evaluated logPDF
*
* @example
* var y = logpdf( 0.5, 1.0, 1.0 );
* // returns 0.0
*
* @example
* var y = logpdf( 0.5, 2.0, 4.0 );
* // returns ~0.523
*
* @example
* var y = logpdf( 0.2, 2.0, 2.0 );
* // returns ~-0.264
*
* @example
* var y = logpdf( 0.8, 4.0, 4.0 );
* // returns ~0.522
*
* @example
* var y = logpdf( -0.5, 4.0, 2.0 );
* // returns -Infinity
*
* @example
* var y = logpdf( 1.5, 4.0, 2.0 );
* // returns -Infinity
*
* @example
* var y = logpdf( 2.0, -1.0, 0.5 );
* // returns NaN
*
* @example
* var y = logpdf( 2.0, 0.5, -1.0 );
* // returns NaN
*
* @example
* var y = logpdf( NaN, 1.0, 1.0 );
* // returns NaN
*
* @example
* var y = logpdf( 0.0, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = logpdf( 0.0, 1.0, NaN );
* // returns NaN
*/
function logpdf( x, a, b ) {
var out;
if (
isnan( x ) ||
isnan( a ) ||
isnan( b ) ||
a <= 0.0 ||
b <= 0.0
) {
return NaN;
}
if ( x < 0.0 || x > 1.0 ) {
return NINF;
}
// At the boundaries of the support, the density is infinite, finite, or zero depending on whether the corresponding shape parameter is less than, equal to, or greater than one:
if ( x === 0.0 ) {
if ( a < 1.0 ) {
return PINF;
}
if ( a > 1.0 ) {
return NINF;
}
return ln( b );
}
if ( x === 1.0 ) {
if ( b < 1.0 ) {
return PINF;
}
if ( b > 1.0 ) {
return NINF;
}
return ln( a );
}
out = ln( a*b );
out += ( a - 1.0 ) * ln( x );
out += ( b - 1.0 ) * ln( 1.0 - pow( x, a ) );
return out;
}
// EXPORTS //
module.exports = logpdf;
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