README.md (3618B)
1 <!-- 2 3 @license Apache-2.0 4 5 Copyright (c) 2018 The Stdlib Authors. 6 7 Licensed under the Apache License, Version 2.0 (the "License"); 8 you may not use this file except in compliance with the License. 9 You may obtain a copy of the License at 10 11 http://www.apache.org/licenses/LICENSE-2.0 12 13 Unless required by applicable law or agreed to in writing, software 14 distributed under the License is distributed on an "AS IS" BASIS, 15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 16 See the License for the specific language governing permissions and 17 limitations under the License. 18 19 --> 20 21 # Probability Density Function 22 23 > [Laplace][laplace-distribution] distribution probability density function (PDF). 24 25 <section class="intro"> 26 27 The [probability density function][pdf] (PDF) for a [Laplace][laplace-distribution] random variable is 28 29 <!-- <equation class="equation" label="eq:laplace_pdf" align="center" raw="f(x\mid\mu,b) = \frac{1}{2b} \exp \left( -\frac{|x-\mu|}{b} \right)" alt="Probability density function (PDF) for a Laplace distribution."> --> 30 31 <div class="equation" align="center" data-raw-text="f(x\mid\mu,b) = \frac{1}{2b} \exp \left( -\frac{|x-\mu|}{b} \right)" data-equation="eq:laplace_pdf"> 32 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/laplace/pdf/docs/img/equation_laplace_pdf.svg" alt="Probability density function (PDF) for a Laplace distribution."> 33 <br> 34 </div> 35 36 <!-- </equation> --> 37 38 where `mu` is the location parameter and `b > 0` is the scale parameter (also called diversity). 39 40 </section> 41 42 <!-- /.intro --> 43 44 <section class="usage"> 45 46 ## Usage 47 48 ```javascript 49 var pdf = require( '@stdlib/stats/base/dists/laplace/pdf' ); 50 ``` 51 52 #### pdf( x, mu, b ) 53 54 Evaluates the [probability density function][pdf] (PDF) for a [Laplace][laplace-distribution] distribution with parameters `mu` (location parameter) and `b > 0` (scale parameter). 55 56 ```javascript 57 var y = pdf( 2.0, 0.0, 1.0 ); 58 // returns ~0.068 59 60 y = pdf( -1.0, 2.0, 3.0 ); 61 // returns ~0.061 62 63 y = pdf( 2.5, 2.0, 3.0 ); 64 // returns ~0.141 65 ``` 66 67 If provided `NaN` as any argument, the function returns `NaN`. 68 69 ```javascript 70 var y = pdf( NaN, 0.0, 1.0 ); 71 // returns NaN 72 73 y = pdf( 0.0, NaN, 1.0 ); 74 // returns NaN 75 76 y = pdf( 0.0, 0.0, NaN ); 77 // returns NaN 78 ``` 79 80 If provided `b <= 0`, the function returns `NaN`. 81 82 ```javascript 83 var y = pdf( 2.0, 0.0, -1.0 ); 84 // returns NaN 85 86 y = pdf( 2.0, 8.0, 0.0 ); 87 // returns NaN 88 ``` 89 90 #### pdf.factory( mu, b ) 91 92 Returns a `function` for evaluating the [PDF][pdf] of a [Laplace][laplace-distribution] distribution with parameters `mu` (location parameter) and `b > 0` (scale parameter). 93 94 ```javascript 95 var mypdf = pdf.factory( 10.0, 2.0 ); 96 97 var y = mypdf( 10.0 ); 98 // returns 0.25 99 100 y = mypdf( 5.0 ); 101 // returns ~0.021 102 103 y = mypdf( 12.0 ); 104 // returns ~0.092 105 ``` 106 107 </section> 108 109 <!-- /.usage --> 110 111 <section class="examples"> 112 113 ## Examples 114 115 <!-- eslint no-undef: "error" --> 116 117 ```javascript 118 var randu = require( '@stdlib/random/base/randu' ); 119 var pdf = require( '@stdlib/stats/base/dists/laplace/pdf' ); 120 121 var mu; 122 var b; 123 var x; 124 var y; 125 var i; 126 127 for ( i = 0; i < 100; i++ ) { 128 x = randu() * 10.0; 129 mu = randu() * 10.0; 130 b = randu() * 10.0; 131 y = pdf( x, mu, b ); 132 console.log( 'x: %d, µ: %d, b: %d, f(x;µ,b): %d', x.toFixed( 4 ), mu.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) ); 133 } 134 ``` 135 136 </section> 137 138 <!-- /.examples --> 139 140 <section class="links"> 141 142 [laplace-distribution]: https://en.wikipedia.org/wiki/Laplace_distribution 143 144 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function 145 146 </section> 147 148 <!-- /.links -->