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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 NINF = require( '@stdlib/constants/float64/ninf' );
// MAIN //
/**
* Evaluates the natural logarithm of the probability density function (PDF) for a Pareto (Type I) distribution with shape parameter `alpha` and scale parameter `beta` at a value `x`.
*
* @param {number} x - input value
* @param {PositiveNumber} alpha - shape parameter
* @param {PositiveNumber} beta - scale parameter
* @returns {number} evaluated logPDF
*
* @example
* var y = logpdf( 4.0, 1.0, 1.0 );
* // returns ~-2.773
*
* @example
* var y = logpdf( 20.0, 1.0, 10.0 );
* // returns ~-3.689
*
* @example
* var y = logpdf( 7.0, 2.0, 6.0 );
* // returns ~-1.561
*
* @example
* var y = logpdf( 7.0, 6.0, 3.0 );
* // returns ~-5.238
*
* @example
* var y = logpdf( 1.0, 4.0, 2.0 );
* // returns -Infinity
*
* @example
* var y = logpdf( 1.5, 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 denom;
var num;
if (
isnan( x ) ||
isnan( alpha ) ||
isnan( beta ) ||
alpha <= 0.0 ||
beta <= 0.0
) {
return NaN;
}
if ( x >= beta ) {
num = ln( alpha ) + ( alpha * ln( beta ) );
denom = ( alpha + 1.0 ) * ln( x );
return num - denom;
}
return NINF;
}
// EXPORTS //
module.exports = logpdf;
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