README.md (6621B)
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 # Lognormal 22 23 > Lognormal distribution constructor. 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 </section> 30 31 <!-- /.intro --> 32 33 <!-- Package usage documentation. --> 34 35 <section class="usage"> 36 37 ## Usage 38 39 ```javascript 40 var LogNormal = require( '@stdlib/stats/base/dists/lognormal/ctor' ); 41 ``` 42 43 #### LogNormal( \[mu, sigma] ) 44 45 Returns a [lognormal][lognormal-distribution] distribution object. 46 47 ```javascript 48 var lognormal = new LogNormal(); 49 50 var mean = lognormal.mean; 51 // returns ~1.649 52 ``` 53 54 By default, `mu = 0.0` and `sigma = 1.0`. To create a distribution having a different `mu` (location parameter) and `sigma` (scale parameter), provide the corresponding arguments. 55 56 ```javascript 57 var lognormal = new LogNormal( 2.0, 4.0 ); 58 59 var mu = lognormal.mean; 60 // returns ~22026.466 61 ``` 62 63 * * * 64 65 ## lognormal 66 67 A [lognormal][lognormal-distribution] distribution object has the following properties and methods... 68 69 ### Writable Properties 70 71 #### lognormal.mu 72 73 Location parameter of the distribution. 74 75 ```javascript 76 var lognormal = new LogNormal(); 77 78 var mu = lognormal.mu; 79 // returns 0.0 80 81 lognormal.mu = 3.0; 82 83 mu = lognormal.mu; 84 // returns 3.0 85 ``` 86 87 #### lognormal.sigma 88 89 Scale parameter of the distribution. `sigma` **must** be a positive number. 90 91 ```javascript 92 var lognormal = new LogNormal( 2.0, 4.0 ); 93 94 var sigma = lognormal.sigma; 95 // returns 4.0 96 97 lognormal.sigma = 3.0; 98 99 sigma = lognormal.sigma; 100 // returns 3.0 101 ``` 102 103 * * * 104 105 ### Computed Properties 106 107 #### LogNormal.prototype.entropy 108 109 Returns the [differential entropy][entropy]. 110 111 ```javascript 112 var lognormal = new LogNormal( 4.0, 12.0 ); 113 114 var entropy = lognormal.entropy; 115 // returns ~7.904 116 ``` 117 118 #### LogNormal.prototype.kurtosis 119 120 Returns the [excess kurtosis][kurtosis]. 121 122 ```javascript 123 var lognormal = new LogNormal( 4.0, 12.0 ); 124 125 var kurtosis = lognormal.kurtosis; 126 // returns 1.4243659274306933e+250 127 ``` 128 129 #### LogNormal.prototype.mean 130 131 Returns the [expected value][expected-value]. 132 133 ```javascript 134 var lognormal = new LogNormal( 4.0, 12.0 ); 135 136 var mu = lognormal.mean; 137 // returns 1.0148003881138887e+33 138 ``` 139 140 #### LogNormal.prototype.median 141 142 Returns the [median][median]. 143 144 ```javascript 145 var lognormal = new LogNormal( 4.0, 12.0 ); 146 147 var median = lognormal.median; 148 // returns ~54.598 149 ``` 150 151 #### LogNormal.prototype.mode 152 153 Returns the [mode][mode]. 154 155 ```javascript 156 var lognormal = new LogNormal( 4.0, 12.0 ); 157 158 var mode = lognormal.mode; 159 // returns 1.580420060273613e-61 160 ``` 161 162 #### LogNormal.prototype.skewness 163 164 Returns the [skewness][skewness]. 165 166 ```javascript 167 var lognormal = new LogNormal( 4.0, 12.0 ); 168 169 var skewness = lognormal.skewness; 170 // returns 6.421080152185613e+93 171 ``` 172 173 #### LogNormal.prototype.stdev 174 175 Returns the [standard deviation][standard-deviation]. 176 177 ```javascript 178 var lognormal = new LogNormal( 4.0, 12.0 ); 179 180 var s = lognormal.stdev; 181 // returns 1.886180808490652e+64 182 ``` 183 184 #### LogNormal.prototype.variance 185 186 Returns the [variance][variance]. 187 188 ```javascript 189 var lognormal = new LogNormal( 4.0, 12.0 ); 190 191 var s2 = lognormal.variance; 192 // returns 3.55767804231845e+128 193 ``` 194 195 * * * 196 197 ### Methods 198 199 #### LogNormal.prototype.cdf( x ) 200 201 Evaluates the [cumulative distribution function][cdf] (CDF). 202 203 ```javascript 204 var lognormal = new LogNormal( 2.0, 4.0 ); 205 206 var y = lognormal.cdf( 0.5 ); 207 // returns ~0.25 208 ``` 209 210 #### LogNormal.prototype.logpdf( x ) 211 212 Evaluates the natural logarithm of the [probability density function][pdf] (PDF). 213 214 ```javascript 215 var lognormal = new LogNormal( 2.0, 4.0 ); 216 217 var y = lognormal.logpdf( 2.0 ); 218 // returns ~-3.052 219 ``` 220 221 #### LogNormal.prototype.pdf( x ) 222 223 Evaluates the [probability density function][pdf] (PDF). 224 225 ```javascript 226 var lognormal = new LogNormal( 2.0, 4.0 ); 227 228 var y = lognormal.pdf( 2.0 ); 229 // returns ~0.047 230 ``` 231 232 #### LogNormal.prototype.quantile( p ) 233 234 Evaluates the [quantile function][quantile-function] at probability `p`. 235 236 ```javascript 237 var lognormal = new LogNormal( 2.0, 4.0 ); 238 239 var y = lognormal.quantile( 0.5 ); 240 // returns ~7.389 241 242 y = lognormal.quantile( 1.9 ); 243 // returns NaN 244 ``` 245 246 </section> 247 248 <!-- /.usage --> 249 250 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> 251 252 <section class="notes"> 253 254 </section> 255 256 <!-- /.notes --> 257 258 <!-- Package usage examples. --> 259 260 * * * 261 262 <section class="examples"> 263 264 ## Examples 265 266 <!-- eslint no-undef: "error" --> 267 268 ```javascript 269 var LogNormal = require( '@stdlib/stats/base/dists/lognormal/ctor' ); 270 271 var lognormal = new LogNormal( 2.0, 1.0 ); 272 273 var mean = lognormal.mean; 274 // returns ~12.182 275 276 var median = lognormal.median; 277 // returns ~7.389 278 279 var s2 = lognormal.variance; 280 // returns ~255.016 281 282 var y = lognormal.cdf( 0.8 ); 283 // returns ~0.013 284 ``` 285 286 </section> 287 288 <!-- /.examples --> 289 290 <!-- 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. --> 291 292 <section class="references"> 293 294 </section> 295 296 <!-- /.references --> 297 298 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> 299 300 <section class="links"> 301 302 [lognormal-distribution]: https://en.wikipedia.org/wiki/Log-normal_distribution 303 304 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function 305 306 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function 307 308 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function 309 310 [entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29 311 312 [expected-value]: https://en.wikipedia.org/wiki/Expected_value 313 314 [kurtosis]: https://en.wikipedia.org/wiki/Kurtosis 315 316 [median]: https://en.wikipedia.org/wiki/Median 317 318 [mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29 319 320 [skewness]: https://en.wikipedia.org/wiki/Skewness 321 322 [standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation 323 324 [variance]: https://en.wikipedia.org/wiki/Variance 325 326 </section> 327 328 <!-- /.links -->