@stdlib/stats/base/dists/frechet/logpdf/lib/main.js

Standard library statistical functions.

/**
* @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 NINF = require( '@stdlib/constants/float64/ninf' );


// MAIN //

/**
* Evaluates the logarithm of the probability density function (PDF) for a Fréchet distribution with shape `alpha`, scale `s`, and location `m` at a value `x`.
*
* @param {number} x - input value
* @param {PositiveNumber} alpha - shape parameter
* @param {PositiveNumber} s - scale parameter
* @param {number} m - location parameter
* @returns {number} evaluated logPDF
*
* @example
* var y = logpdf( 10.0, 2.0, 3.0, 2.0 );
* // returns ~-3.489
*
* @example
* var y = logpdf( -2.0, 1.0, 3.0, -3.0 );
* // returns ~-1.901
*
* @example
* var y = logpdf( 0.0, 2.0, 1.0, 1.0 );
* // returns -Infinity
*
* @example
* var y = logpdf( NaN, 2.0, 1.0, -1.0 );
* // returns NaN
*
* @example
* var y = logpdf( 0.0, NaN, 1.0, -1.0 );
* // returns NaN
*
* @example
* var y = logpdf( 0.0, 2.0, NaN, -1.0 );
* // returns NaN
*
* @example
* var y = logpdf( 0.0, 2.0, 1.0, NaN );
* // returns NaN
*
* @example
* var y = logpdf( 0.0, -1.0, 1.0, 0.0 );
* // returns NaN
*
* @example
* var y = logpdf( 0.0, 1.0, -1.0, 0.0 );
* // returns NaN
*/
function logpdf( x, alpha, s, m ) {
	var z;
	if (
		isnan( x ) ||
		isnan( alpha ) ||
		isnan( s ) ||
		isnan( m ) ||
		alpha <= 0.0 ||
		s <= 0.0
	) {
		return NaN;
	}
	if ( x <= m ) {
		return NINF;
	}
	z = ( x - m ) / s;
	return ln( alpha/s ) - ( ( 1.0+alpha ) * ln( z ) ) - pow( z, -alpha );
}


// EXPORTS //

module.exports = logpdf;