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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 exp = require( '@stdlib/math/base/special/exp' );
var abs2 = require( '@stdlib/math/base/special/abs2' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var normal = require( '@stdlib/stats/base/dists/normal/cdf' ).factory;
var SQRT_TWO_PI = require( '@stdlib/constants/float64/sqrt-two-pi' );
// VARIABLES //
var normalCDF = normal( 0.0, 1.0 );
// MAIN //
/**
* Evaluates the probability density function (PDF) for a truncated normal distribution with endpoints `a` and `b`, location parameter `mu` and scale parameter `sigma` at a value `x`.
*
* @param {number} x - input value
* @param {number} a - minimum support
* @param {number} b - maximum support
* @param {number} mu - location parameter
* @param {PositiveNumber} sigma - scale parameter
* @returns {number} evaluated PDF
*
* @example
* var y = pdf( 0.9, 0.0, 1.0, 0.0, 1.0 );
* // returns ~0.7795
*
* @example
* var y = pdf( 0.9, 0.0, 1.0, 0.5, 1.0 );
* // returns ~0.9617
*
* @example
* var y = pdf( 0.9, -1.0, 1.0, 0.5, 1.0 );
* // returns ~0.5896
*
* @example
* var y = pdf( 1.4, 0.0, 1.0, 0.0, 1.0 );
* // returns 0.0
*
* @example
* var y = pdf( -0.9, 0.0, 1.0, 0.0, 1.0 );
* // returns 0.0
*/
function pdf( x, a, b, mu, sigma ) {
var A;
var C;
if (
isnan( x ) ||
isnan( a ) ||
isnan( b ) ||
sigma <= 0.0 ||
a >= b
) {
return NaN;
}
if ( x < a || x > b ) {
return 0.0;
}
A = 1.0 / ( sigma * SQRT_TWO_PI );
C = normalCDF( (b-mu)/sigma ) - normalCDF( (a-mu)/sigma );
return A * exp( -0.5 * abs2( ( x - mu ) / sigma ) ) / C;
}
// EXPORTS //
module.exports = pdf;
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