Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 | 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x | /**
* @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 pow = require( '@stdlib/math/base/special/pow' );
// MAIN //
/**
* Evaluates the probability density function (PDF) for a Pareto (Type I) distribution with shape parameter `alpha` and scale parameter `beta` at a value `x`.
*
* @param {number} x - input value
* @param {PositiveNumber} alpha - shape parameter
* @param {PositiveNumber} beta - scale parameter
* @returns {number} evaluated PDF
*
* @example
* var y = pdf( 4.0, 1.0, 1.0 );
* // returns ~0.063
*
* @example
* var y = pdf( 20.0, 1.0, 10.0 );
* // returns 0.025
*
* @example
* var y = pdf( 7.0, 2.0, 6.0 );
* // returns ~0.21
*
* @example
* var y = pdf( 7.0, 6.0, 3.0 );
* // returns ~0.005
*
* @example
* var y = pdf( 1.0, 4.0, 2.0 );
* // returns 0.0
*
* @example
* var y = pdf( 1.5, 4.0, 2.0 );
* // returns 0.0
*
* @example
* var y = pdf( 0.5, -1.0, 0.5 );
* // returns NaN
*
* @example
* var y = pdf( 0.5, 0.5, -1.0 );
* // returns NaN
*
* @example
* var y = pdf( NaN, 1.0, 1.0 );
* // returns NaN
*
* @example
* var y = pdf( 0.5, NaN, 1.0 );
* // returns NaN
*
* @example
* var y = pdf( 0.5, 1.0, NaN );
* // returns NaN
*/
function pdf( x, alpha, beta ) {
var denom;
var num;
if (
isnan( x ) ||
isnan( alpha ) ||
isnan( beta ) ||
alpha <= 0.0 ||
beta <= 0.0
) {
return NaN;
}
if ( x >= beta ) {
num = alpha * pow( beta, alpha );
denom = pow( x, alpha + 1.0 );
return num / denom;
}
return 0.0;
}
// EXPORTS //
module.exports = pdf;
|