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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 expm1 = require( '@stdlib/math/base/special/expm1' );
var pow = require( '@stdlib/math/base/special/pow' );
// MAIN //
/**
* Evaluates the cumulative distribution function (CDF) for a Rayleigh distribution with scale parameter `sigma` at a value `x`.
*
* @param {number} x - input value
* @param {NonNegativeNumber} sigma - scale parameter
* @returns {Probability} evaluated CDF
*
* @example
* var y = cdf( 2.0, 3.0 );
* // returns ~0.199
*
* @example
* var y = cdf( 1.0, 2.0 );
* // returns ~0.118
*
* @example
* var y = cdf( -1.0, 4.0 );
* // returns 0.0
*
* @example
* var y = cdf( NaN, 1.0 );
* // returns NaN
*
* @example
* var y = cdf( 0.0, NaN );
* // returns NaN
*
* @example
* // Negative scale parameter:
* var y = cdf( 2.0, -1.0 );
* // returns NaN
*/
function cdf( x, sigma ) {
if (
isnan( x ) ||
isnan( sigma ) ||
sigma < 0.0
) {
return NaN;
}
if ( sigma === 0.0 ) {
return ( x < 0.0 ) ? 0.0 : 1.0;
}
if ( x < 0.0 ) {
return 0.0;
}
return -expm1( -0.5 * pow( x / sigma, 2.0 ) );
}
// EXPORTS //
module.exports = cdf;
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