README.md (4366B)
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 # Logarithm of Cumulative Distribution Function 22 23 > [Weibull][weibull-distribution] distribution logarithm of [cumulative distribution function][cdf]. 24 25 <section class="intro"> 26 27 The [cumulative distribution function][cdf] for a [Weibull][weibull-distribution] random variable is 28 29 <!-- <equation class="equation" label="eq:weibull_cdf" align="center" raw="F(x;\lambda, k) =\begin{cases}1- e^{-(x/\lambda)^k} & x\geq0\\ 0 & x<0\end{cases}" alt="Cumulative distribution function for a Weibull distribution."> --> 30 31 <div class="equation" align="center" data-raw-text="F(x;\lambda, k) =\begin{cases}1- e^{-(x/\lambda)^k} & x\geq0\\ 0 & x<0\end{cases}" data-equation="eq:weibull_cdf"> 32 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@e2f64e6ec3d2c31743d067b73ccd26699c52be67/lib/node_modules/@stdlib/stats/base/dists/weibull/logcdf/docs/img/equation_weibull_cdf.svg" alt="Cumulative distribution function for a Weibull distribution."> 33 <br> 34 </div> 35 36 <!-- </equation> --> 37 38 where `lambda > 0` is the [shape parameter][shape] and `k > 0` is the [scale parameter][scale]. 39 40 </section> 41 42 <!-- /.intro --> 43 44 <section class="usage"> 45 46 ## Usage 47 48 ```javascript 49 var logcdf = require( '@stdlib/stats/base/dists/weibull/logcdf' ); 50 ``` 51 52 #### logcdf( x, k, lambda ) 53 54 Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF) for a [Weibull][weibull-distribution] distribution with [shape parameter][shape] `k` and [scale parameter][scale] `lambda`. 55 56 ```javascript 57 var y = logcdf( 2.0, 1.0, 0.5 ); 58 // returns ~-0.018 59 60 y = logcdf( 0.0, 0.5, 1.0 ); 61 // returns -Infinity 62 63 y = logcdf( -Infinity, 4.0, 2.0 ); 64 // returns -Infinity 65 66 y = logcdf( +Infinity, 4.0, 2.0 ); 67 // returns 0.0 68 ``` 69 70 If provided `NaN` as any argument, the function returns `NaN`. 71 72 ```javascript 73 var y = logcdf( NaN, 1.0, 1.0 ); 74 // returns NaN 75 76 y = logcdf( 0.0, NaN, 1.0 ); 77 // returns NaN 78 79 y = logcdf( 0.0, 1.0, NaN ); 80 // returns NaN 81 ``` 82 83 If provided `k <= 0`, the function returns `NaN`. 84 85 ```javascript 86 var y = logcdf( 2.0, -1.0, 0.5 ); 87 // returns NaN 88 89 y = logcdf( 2.0, 0.0, 0.5 ); 90 // returns NaN 91 ``` 92 93 If provided `lambda <= 0`, the function returns `NaN`. 94 95 ```javascript 96 var y = logcdf( 2.0, 0.5, -1.0 ); 97 // returns NaN 98 99 y = logcdf( 2.0, 0.5, 0.0 ); 100 // returns NaN 101 ``` 102 103 #### logcdf.factory( k, lambda ) 104 105 Returns a function for evaluating the [cumulative distribution function][cdf] of a [Weibull][weibull-distribution] distribution with [shape parameter][shape] `k` and [scale parameter][scale] `lambda`. 106 107 ```javascript 108 var mylogcdf = logcdf.factory( 2.0, 10.0 ); 109 110 var y = mylogcdf( 10.0 ); 111 // returns ~-0.459 112 113 y = mylogcdf( 8.0 ); 114 // returns ~-0.749 115 ``` 116 117 </section> 118 119 <!-- /.usage --> 120 121 <section class="notes"> 122 123 ## Notes 124 125 - In virtually all cases, using the `logpdf` or `logcdf` functions is preferable to manually computing the logarithm of the `pdf` or `cdf`, respectively, since the latter is prone to overflow and underflow. 126 127 </section> 128 129 <!-- /.notes --> 130 131 <section class="examples"> 132 133 ## Examples 134 135 <!-- eslint no-undef: "error" --> 136 137 ```javascript 138 var randu = require( '@stdlib/random/base/randu' ); 139 var logcdf = require( '@stdlib/stats/base/dists/weibull/logcdf' ); 140 141 var lambda; 142 var k; 143 var x; 144 var y; 145 var i; 146 147 for ( i = 0; i < 10; i++ ) { 148 x = randu() * 10.0; 149 lambda = randu() * 10.0; 150 k = randu() * 10.0; 151 y = logcdf( x, lambda, k ); 152 console.log( 'x: %d, k: %d, λ: %d, ln(F(x;k,λ)): %d', x, k, lambda, y ); 153 } 154 ``` 155 156 </section> 157 158 <!-- /.examples --> 159 160 <section class="links"> 161 162 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function 163 164 [weibull-distribution]: https://en.wikipedia.org/wiki/Weibull_distribution 165 166 [shape]: https://en.wikipedia.org/wiki/Shape_parameter 167 168 [scale]: https://en.wikipedia.org/wiki/Scale_parameter 169 170 </section> 171 172 <!-- /.links -->