README.md (4031B)
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 > [Weibull][weibull-distribution] distribution probability density function (PDF). 24 25 <section class="intro"> 26 27 The [probability density function][pdf] (PDF) for a [Weibull][weibull-distribution] random variable is 28 29 <!-- <equation class="equation" label="eq:weibull_weibull_pdf" align="center" raw="f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left (\frac{x}{\lambda} \right)^{k-1}e^{-(x/\lambda)^k} & x \geq 0 \\ 0 & x < 0\end{cases}" alt="Probability density function (PDF) for a Weibull distribution."> --> 30 31 <div class="equation" align="center" data-raw-text="f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left (\frac{x}{\lambda} \right)^{k-1}e^{-(x/\lambda)^k} & x \geq 0 \\ 0 & x < 0\end{cases}" data-equation="eq:weibull_weibull_pdf"> 32 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/weibull/pdf/docs/img/equation_weibull_weibull_pdf.svg" alt="Probability density function (PDF) for a Weibull distribution."> 33 <br> 34 </div> 35 36 <!-- </equation> --> 37 38 where `lambda > 0` and `k > 0` are the respective [scale][scale] and [shape][shape] parameters of the distribution. 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/weibull/pdf' ); 50 ``` 51 52 #### pdf( x, k, lambda ) 53 54 Evaluates the [probability density function][pdf] (PDF) for a [Weibull][weibull-distribution] distribution with [shape parameter][shape] `k` and [scale parameter][scale] `lambda`. 55 56 ```javascript 57 var y = pdf( 2.0, 1.0, 0.5 ); 58 // returns ~0.037 59 60 y = pdf( -1.0, 4.0, 2.0 ); 61 // returns 0.0 62 ``` 63 64 If provided `NaN` as any argument, the function returns `NaN`. 65 66 ```javascript 67 var y = pdf( NaN, 0.0, 1.0 ); 68 // returns NaN 69 70 y = pdf( 0.0, NaN, 1.0 ); 71 // returns NaN 72 73 y = pdf( 0.0, 0.0, NaN ); 74 // returns NaN 75 ``` 76 77 If provided `k <= 0`, the function returns `NaN`. 78 79 ```javascript 80 var y = pdf( 2.0, 0.0, 1.0 ); 81 // returns NaN 82 83 y = pdf( 2.0, -1.0, 1.0 ); 84 // returns NaN 85 ``` 86 87 If provided `lambda <= 0`, the function returns `NaN`. 88 89 ```javascript 90 var y = pdf( 2.0, 1.0, 0.0 ); 91 // returns NaN 92 93 y = pdf( 2.0, 1.0, -1.0 ); 94 // returns NaN 95 ``` 96 97 #### pdf.factory( k, lambda ) 98 99 Returns a `function` for evaluating the [PDF][pdf] for a [Weibull][weibull-distribution] distribution with [shape parameter][shape] `k` and [scale parameter][scale] `lambda`. 100 101 ```javascript 102 var mypdf = pdf.factory( 2.0, 10.0 ); 103 104 var y = mypdf( 12.0 ); 105 // returns ~0.057 106 107 y = mypdf( 5.0 ); 108 // returns ~0.078 109 ``` 110 111 </section> 112 113 <!-- /.usage --> 114 115 <section class="examples"> 116 117 ## Examples 118 119 <!-- eslint no-undef: "error" --> 120 121 ```javascript 122 var randu = require( '@stdlib/random/base/randu' ); 123 var pdf = require( '@stdlib/stats/base/dists/weibull/pdf' ); 124 125 var lambda; 126 var k; 127 var x; 128 var y; 129 var i; 130 131 for ( i = 0; i < 10; i++ ) { 132 x = randu() * 10.0; 133 lambda = randu() * 10.0; 134 k = randu() * 10.0; 135 y = pdf( x, lambda, k ); 136 console.log( 'x: %d, k: %d, λ: %d, f(x;k,λ): %d', x.toFixed( 4 ), k.toFixed( 4 ), lambda.toFixed( 4 ), y.toFixed( 4 ) ); 137 } 138 ``` 139 140 </section> 141 142 <!-- /.examples --> 143 144 <section class="links"> 145 146 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function 147 148 [weibull-distribution]: https://en.wikipedia.org/wiki/Weibull_distribution 149 150 [shape]: https://en.wikipedia.org/wiki/Shape_parameter 151 152 [scale]: https://en.wikipedia.org/wiki/Scale_parameter 153 154 </section> 155 156 <!-- /.links -->