README.md (3265B)
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 > [Exponential][exponential-distribution] distribution probability density function (PDF). 24 25 <section class="intro"> 26 27 The [probability density function][pdf] (PDF) for an [exponential][exponential-distribution] random variable is 28 29 <!-- <equation class="equation" label="eq:exponential_pdf" align="center" raw="f(x;\lambda) = \begin{cases} \lambda e^{-\lambda x} & x \ge 0 \\ 0 & x < 0 \end{cases}" alt="Probability density function (PDF) for a Exponential distribution."> --> 30 31 <div class="equation" align="center" data-raw-text="f(x;\lambda) = \begin{cases} \lambda e^{-\lambda x} & x \ge 0 \\ 0 & x < 0 \end{cases}" data-equation="eq:exponential_pdf"> 32 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/exponential/pdf/docs/img/equation_exponential_pdf.svg" alt="Probability density function (PDF) for a Exponential distribution."> 33 <br> 34 </div> 35 36 <!-- </equation> --> 37 38 where `λ` is the rate parameter. 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/exponential/pdf' ); 50 ``` 51 52 #### pdf( x, lambda ) 53 54 Evaluates the [probability density function][pdf] (PDF) for an [exponential][exponential-distribution] distribution with rate parameter `lambda`. 55 56 ```javascript 57 var y = pdf( 2.0, 0.3 ); 58 // returns ~0.165 59 60 y = pdf( 2.0, 1.0 ); 61 // returns ~0.135 62 ``` 63 64 If provided `NaN` as any argument, the function returns `NaN`. 65 66 ```javascript 67 var y = pdf( NaN, 0.0 ); 68 // returns NaN 69 70 y = pdf( 0.0, NaN ); 71 // returns NaN 72 ``` 73 74 If provided `lambda < 0`, the function returns `NaN`. 75 76 ```javascript 77 var y = pdf( 2.0, -1.0 ); 78 // returns NaN 79 ``` 80 81 #### pdf.factory( lambda ) 82 83 Partially apply `lambda` to create a reusable `function` for evaluating the [PDF][pdf]. 84 85 ```javascript 86 var mypdf = pdf.factory( 0.1 ); 87 88 var y = mypdf( 8.0 ); 89 // returns ~0.045 90 91 y = mypdf( 5.0 ); 92 // returns ~0.06 93 ``` 94 95 </section> 96 97 <!-- /.usage --> 98 99 <section class="examples"> 100 101 ## Examples 102 103 <!-- eslint no-undef: "error" --> 104 105 ```javascript 106 var randu = require( '@stdlib/random/base/randu' ); 107 var pdf = require( '@stdlib/stats/base/dists/exponential/pdf' ); 108 109 var lambda; 110 var x; 111 var y; 112 var i; 113 114 for ( i = 0; i < 10; i++ ) { 115 x = randu() * 10.0; 116 lambda = randu() * 10.0; 117 y = pdf( x, lambda ); 118 console.log( 'x: %d, λ: %d, f(x;λ): %d', x, lambda, y ); 119 } 120 ``` 121 122 </section> 123 124 <!-- /.examples --> 125 126 <section class="links"> 127 128 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function 129 130 [exponential-distribution]: https://en.wikipedia.org/wiki/Exponential_distribution 131 132 </section> 133 134 <!-- /.links -->