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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 PI = require( '@stdlib/constants/float64/pi' );
// MAIN //
/**
* Returns a function for evaluating the probability density function (PDF) for a Cauchy distribution with location parameter `x0` and scale parameter `gamma`.
*
* @param {number} x0 - location parameter
* @param {PositiveNumber} gamma - scale parameter
* @returns {Function} PDF
*
* @example
* var pdf = factory( 4.0, 2.0 );
*
* var y = pdf( 10.0 );
* // returns ~0.0159
*
* y = pdf( 3.0 );
* // returns ~0.127
*/
function factory( x0, gamma ) {
var gpi;
if (
isnan( gamma ) ||
isnan( x0 ) ||
gamma <= 0.0
) {
return constantFunction( NaN );
}
gpi = gamma * PI;
return pdf;
/**
* Evaluates the probability density function (PDF) for a Cauchy distribution.
*
* @private
* @param {number} x - input value
* @returns {number} evaluated PDF
*
* @example
* var y = pdf( 2.3 );
* // returns <number>
*/
function pdf( x ) {
if ( isnan( x ) ) {
return NaN;
}
return 1.0 / ( gpi * (1.0 + pow( (x-x0)/gamma, 2.0 )) );
}
}
// EXPORTS //
module.exports = factory;
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