README.md (4369B)
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 # Mode 22 23 > [Weibull][weibull-distribution] distribution [mode][mode]. 24 25 <!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. --> 26 27 <section class="intro"> 28 29 The [mode][mode] for a [Weibull][weibull-distribution] random variable is 30 31 <!-- <equation class="equation" label="eq:weibull_mode" align="center" raw="\operatorname{mode}\left( X \right) = {\displaystyle {\begin{cases}\lambda \left({\frac {k-1}{k}}\right)^{\frac {1}{k}}\,&k>1\\0&k\leq 1\end{cases}}}" alt="Mode for a Weibull distribution."> --> 32 33 <div class="equation" align="center" data-raw-text="\operatorname{mode}\left( X \right) = {\displaystyle {\begin{cases}\lambda \left({\frac {k-1}{k}}\right)^{\frac {1}{k}}\,&k>1\\0&k\leq 1\end{cases}}}" data-equation="eq:weibull_mode"> 34 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/weibull/mode/docs/img/equation_weibull_mode.svg" alt="Mode for a Weibull distribution."> 35 <br> 36 </div> 37 38 <!-- </equation> --> 39 40 where `λ > 0` is the [shape parameter][shape] and `k > 0` is the [scale parameter][scale]. 41 42 </section> 43 44 <!-- /.intro --> 45 46 <!-- Package usage documentation. --> 47 48 <section class="usage"> 49 50 ## Usage 51 52 ```javascript 53 var mode = require( '@stdlib/stats/base/dists/weibull/mode' ); 54 ``` 55 56 #### mode( k, lambda ) 57 58 Returns the [mode][mode] of a [Weibull][weibull-distribution] distribution with parameters `k` (shape parameter) and `lambda` (scale parameter). 59 60 ```javascript 61 var v = mode( 4.0, 12.0 ); 62 // returns ~11.167 63 64 v = mode( 8.0, 2.0 ); 65 // returns ~1.967 66 ``` 67 68 If provided `0 < k <= 1`, the function returns `0.0`. 69 70 ```javascript 71 var v = mode( 1.0, 1.0 ); 72 // returns 0.0 73 ``` 74 75 If provided `NaN` as any argument, the function returns `NaN`. 76 77 ```javascript 78 var v = mode( NaN, 2.0 ); 79 // returns NaN 80 81 v = mode( 2.0, NaN ); 82 // returns NaN 83 ``` 84 85 If provided `k <= 0`, the function returns `NaN`. 86 87 ```javascript 88 var v = mode( 0.0, 1.0 ); 89 // returns NaN 90 91 v = mode( -1.0, 1.0 ); 92 // returns NaN 93 ``` 94 95 If provided `lambda <= 0`, the function returns `NaN`. 96 97 ```javascript 98 var v = mode( 1.0, 0.0 ); 99 // returns NaN 100 101 v = mode( 1.0, -1.0 ); 102 // returns NaN 103 ``` 104 105 </section> 106 107 <!-- /.usage --> 108 109 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> 110 111 <section class="notes"> 112 113 </section> 114 115 <!-- /.notes --> 116 117 <!-- Package usage examples. --> 118 119 <section class="examples"> 120 121 ## Examples 122 123 <!-- eslint no-undef: "error" --> 124 125 ```javascript 126 var randu = require( '@stdlib/random/base/randu' ); 127 var EPS = require( '@stdlib/constants/float64/eps' ); 128 var mode = require( '@stdlib/stats/base/dists/weibull/mode' ); 129 130 var lambda; 131 var k; 132 var v; 133 var i; 134 135 for ( i = 0; i < 10; i++ ) { 136 k = ( randu()*10.0 ) + EPS; 137 lambda = ( randu()*10.0 ) + EPS; 138 v = mode( k, lambda ); 139 console.log( 'k: %d, λ: %d, mode(X;k,λ): %d', k.toFixed( 4 ), lambda.toFixed( 4 ), v.toFixed( 4 ) ); 140 } 141 ``` 142 143 </section> 144 145 <!-- /.examples --> 146 147 <!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> 148 149 <section class="references"> 150 151 </section> 152 153 <!-- /.references --> 154 155 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> 156 157 <section class="links"> 158 159 [weibull-distribution]: https://en.wikipedia.org/wiki/Weibull_distribution 160 161 [mode]: https://en.wikipedia.org/wiki/Mode 162 163 [shape]: https://en.wikipedia.org/wiki/Shape_parameter 164 165 [scale]: https://en.wikipedia.org/wiki/Scale_parameter 166 167 </section> 168 169 <!-- /.links -->