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* @license Apache-2.0
*
* Copyright (c) 2026 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_TWO_PI = require( '@stdlib/constants/float64/ln-two-pi' );
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 Wald distribution with mean `mu` and shape parameter `lambda` at a value `x`.
*
* @param {number} x - input value
* @param {PositiveNumber} mu - mean
* @param {NonNegativeNumber} lambda - shape parameter
* @returns {number} evaluated logPDF
*
* @example
* var y = logpdf( 2.0, 1.0, 1.0 );
* // returns ~-2.209
*
* @example
* var y = logpdf( 0.5, 2.0, 3.0 );
* // returns ~-1.017
*
* @example
* var y = logpdf( NaN, 1.0, 1.0 );
* // returns NaN
*
* @example
* var y = logpdf( 1.0, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = logpdf( 1.0, 1.0, NaN );
* // returns NaN
*
* @example
* // Non-positive mean:
* var y = logpdf( 2.0, 0.0, 1.0 );
* // returns NaN
*
* @example
* // Negative shape parameter:
* var y = logpdf( 2.0, 1.0, -1.0 );
* // returns NaN
*
* @example
* // Zero shape parameter (degenerate distribution):
* var y = logpdf( 1.0, 1.0, 0.0 );
* // returns Infinity
*
* @example
* var y = logpdf( 0.0, 1.0, 1.0 );
* // returns -Infinity
*/
function logpdf( x, mu, lambda ) {
var v;
if (
isnan( x ) ||
isnan( mu ) ||
isnan( lambda ) ||
mu <= 0.0 ||
lambda < 0.0
) {
return NaN;
}
if ( lambda === 0.0 ) {
return ( x === mu ) ? PINF : NINF;
}
if ( x <= 0.0 || x === PINF ) {
return NINF;
}
v = x - mu;
return 0.5 * ( ln( lambda ) - ( LN_TWO_PI + ( 3.0 * ln( x ) ) ) - ( ( lambda * v * v ) / ( mu * mu * x ) ) );
}
// EXPORTS //
module.exports = logpdf;
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