README.md (4268B)
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 > [Logistic][logistic-distribution] distribution logarithm of [cumulative distribution function][cdf]. 24 25 <section class="intro"> 26 27 The [cumulative distribution function][cdf] for a [logistic][logistic-distribution] random variable is 28 29 <!-- <equation class="equation" label="eq:logistic_cdf" align="center" raw="F(x; \mu, s) = \frac{1}{1+e^{-\frac{x-\mu}{s}}}" alt="Cumulative distribution function for a logistic distribution."> --> 30 31 <div class="equation" align="center" data-raw-text="F(x; \mu, s) = \frac{1}{1+e^{-\frac{x-\mu}{s}}}" data-equation="eq:logistic_cdf"> 32 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/logistic/logcdf/docs/img/equation_logistic_cdf.svg" alt="Cumulative distribution function for a logistic distribution."> 33 <br> 34 </div> 35 36 <!-- </equation> --> 37 38 where `mu` is the location parameter and `s > 0` is the scale parameter. 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/logistic/logcdf' ); 50 ``` 51 52 #### logcdf( x, mu, s ) 53 54 Evaluates the logarithm of the [cumulative distribution function][cdf] (CDF) for a [logistic][logistic-distribution] distribution with parameters `mu` (location parameter) and `s` (scale parameter). 55 56 ```javascript 57 var y = logcdf( 2.0, 0.0, 1.0 ); 58 // returns ~-0.127 59 60 y = logcdf( 0.0, 0.0, 1.0 ); 61 // returns ~-0.693 62 63 y = logcdf( -1.0, 4.0, 2.0 ); 64 // returns ~-2.579 65 ``` 66 67 If provided `NaN` as any argument, the function returns `NaN`. 68 69 ```javascript 70 var y = logcdf( NaN, 0.0, 1.0 ); 71 // returns NaN 72 73 y = logcdf( 0.0, NaN, 1.0 ); 74 // returns NaN 75 76 y = logcdf( 0.0, 0.0, NaN ); 77 // returns NaN 78 ``` 79 80 If provided `s < 0`, the function returns `NaN`. 81 82 ```javascript 83 var y = logcdf( 2.0, 0.0, -1.0 ); 84 // returns NaN 85 ``` 86 87 If provided `s = 0`, the function evaluates the logarithm of the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`. 88 89 ```javascript 90 var y = logcdf( 2.0, 8.0, 0.0 ); 91 // returns -Infinity 92 93 y = logcdf( 8.0, 8.0, 0.0 ); 94 // returns 0.0 95 96 y = logcdf( 10.0, 8.0, 0.0 ); 97 // returns 0.0 98 ``` 99 100 #### logcdf.factory( mu, s ) 101 102 Returns a function for evaluating the logarithm of the [cumulative distribution function][cdf] of a [logistic][logistic-distribution] distribution with parameters `mu` (location parameter) and `s` (scale parameter). 103 104 ```javascript 105 var mylogcdf = logcdf.factory( 10.0, 2.0 ); 106 107 var y = mylogcdf( 10.0 ); 108 // returns ~-0.693 109 110 y = mylogcdf( 8.0 ); 111 // returns ~-1.313 112 ``` 113 114 </section> 115 116 <!-- /.usage --> 117 118 <section class="notes"> 119 120 ## Notes 121 122 - 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. 123 124 </section> 125 126 <!-- /.notes --> 127 128 <section class="examples"> 129 130 ## Examples 131 132 <!-- eslint no-undef: "error" --> 133 134 ```javascript 135 var randu = require( '@stdlib/random/base/randu' ); 136 var logcdf = require( '@stdlib/stats/base/dists/logistic/logcdf' ); 137 138 var mu; 139 var s; 140 var x; 141 var y; 142 var i; 143 144 for ( i = 0; i < 10; i++ ) { 145 x = randu() * 10.0; 146 mu = randu() * 10.0; 147 s = randu() * 10.0; 148 y = logcdf( x, mu, s ); 149 console.log( 'x: %d, µ: %d, s: %d, ln(F(x;µ,s)): %d', x, mu, s, y ); 150 } 151 ``` 152 153 </section> 154 155 <!-- /.examples --> 156 157 <section class="links"> 158 159 [logistic-distribution]: https://en.wikipedia.org/wiki/Logistic_distribution 160 161 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function 162 163 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution 164 165 </section> 166 167 <!-- /.links -->