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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 constantFunction = require( '@stdlib/utils/constant-function' );
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 //
/**
* Returns a function for evaluating the logarithm of the probability density function (PDF) for a Fréchet distribution with shape `alpha`, scale `s`, and location `m`.
*
* @param {PositiveNumber} alpha - shape parameter
* @param {PositiveNumber} s - scale parameter
* @param {number} m - location parameter
* @returns {Function} logPDF
*
* @example
* var logpdf = factory( 3.0, 3.0, 5.0 );
*
* var y = logpdf( 10.0 );
* // returns ~-2.259
*
* y = logpdf( 7.0 );
* // returns ~-1.753
*/
function factory( alpha, s, m ) {
if (
isnan( alpha ) ||
isnan( s ) ||
isnan( m ) ||
alpha <= 0.0 ||
s <= 0.0
) {
return constantFunction( NaN );
}
return logpdf;
/**
* Evaluates the logarithm of the probability density function (PDF) for a Fréchet distribution.
*
* @private
* @param {number} x - input value
* @returns {number} evaluated logPDF
*
* @example
* var y = logpdf( -2.0 );
* // returns <number>
*/
function logpdf( x ) {
var z;
if ( isnan( x ) ) {
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 = factory;
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