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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 betaln = require( '@stdlib/math/base/special/betaln' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var log1p = require( '@stdlib/math/base/special/log1p' );
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 (logPDF) for a beta prime distribution with first shape parameter `alpha` and second shape parameter `beta` at a value `x`.
*
* @param {number} x - input value
* @param {PositiveNumber} alpha - first shape parameter
* @param {PositiveNumber} beta - second shape parameter
* @returns {number} evaluated logPDF
*
* @example
* var y = logpdf( 0.5, 1.0, 1.0 );
* // returns ~-0.811
*
* @example
* var y = logpdf( 0.5, 2.0, 4.0 );
* // returns ~-0.13
*
* @example
* var y = logpdf( 0.2, 2.0, 2.0 );
* // returns ~-0.547
*
* @example
* var y = logpdf( 0.8, 4.0, 4.0 );
* // returns ~-0.43
*
* @example
* var y = logpdf( -0.5, 4.0, 2.0 );
* // returns -Infinity
*
* @example
* var y = logpdf( 0.5, -1.0, 0.5 );
* // returns NaN
*
* @example
* var y = logpdf( 0.5, 0.5, -1.0 );
* // returns NaN
*
* @example
* var y = logpdf( NaN, 1.0, 1.0 );
* // returns NaN
*
* @example
* var y = logpdf( 0.5, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = logpdf( 0.5, 1.0, NaN );
* // returns NaN
*/
function logpdf( x, alpha, beta ) {
var out;
if (
isnan( x ) ||
isnan( alpha ) ||
isnan( beta ) ||
alpha <= 0.0 ||
beta <= 0.0
) {
return NaN;
}
if ( x < 0.0 ) {
// Support of the beta prime distribution: [0,∞)
return NINF;
}
// At `x = 0`, the density is infinite for `alpha < 1`, `1/B(1,beta) = beta` for `alpha = 1`, and `0` for `alpha > 1`:
if ( x === 0.0 ) {
if ( alpha < 1.0 ) {
return PINF;
}
if ( alpha > 1.0 ) {
return NINF;
}
return ln( beta );
}
out = ( alpha-1.0 ) * ln( x );
out -= ( alpha+beta ) * log1p( x );
out -= betaln( alpha, beta );
return out;
}
// EXPORTS //
module.exports = logpdf;
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