All files / stats/base/dists/levy/pdf/lib main.js

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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 sqrt = require( '@stdlib/math/base/special/sqrt' );
var exp = require( '@stdlib/math/base/special/exp' );
var pow = require( '@stdlib/math/base/special/pow' );
var TWO_PI = require( '@stdlib/constants/float64/two-pi' );
 
 
// MAIN //
 
/**
* Evaluates the probability density function (PDF) for a Lévy distribution with location parameter `mu` and scale parameter `c` at a value `x`.
*
* @param {number} x - input value
* @param {number} mu - location parameter
* @param {PositiveNumber} c - scale parameter
* @returns {number} evaluated PDF
*
* @example
* var y = pdf( 2.0, 0.0, 1.0 );
* // returns ~0.11
*
* @example
* var y = pdf( -1.0, 4.0, 2.0 );
* // returns 0.0
*
* @example
* var y = pdf( NaN, 0.0, 1.0 );
* // returns NaN
*
* @example
* var y = pdf( 0.0, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = pdf( 0.0, 0.0, NaN );
* // returns NaN
*
* @example
* // Negative scale parameter:
* var y = pdf( 2.0, 0.0, -1.0 );
* // returns NaN
*/
function pdf( x, mu, c ) {
	if (
		isnan( x ) ||
		isnan( mu ) ||
		isnan( c ) ||
		c <= 0.0
	) {
		return NaN;
	}
	if ( x <= mu ) {
		return 0.0;
	}
	return sqrt( c/TWO_PI ) * exp( -c / ( 2.0*(x-mu) ) ) / pow( x-mu, 1.5 );
}
 
 
// EXPORTS //
 
module.exports = pdf;