README.md (6812B)
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 # Degenerate 22 23 > Degenerate 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 Degenerate = require( '@stdlib/stats/base/dists/degenerate/ctor' ); 41 ``` 42 43 #### Degenerate( \[mu] ) 44 45 Returns a [Degenerate][degenerate-distribution] distribution object. 46 47 ```javascript 48 var degenerate = new Degenerate(); 49 50 var mean = degenerate.mean; 51 // returns 0.0 52 ``` 53 54 By default, `mu = 0.0`. To create a distribution having a different mean value `mu`, provide a parameter value. 55 56 ```javascript 57 var degenerate = new Degenerate( 20.0 ); 58 59 var mean = degenerate.mean; 60 // returns 20.0 61 ``` 62 63 * * * 64 65 ## degenerate 66 67 A [Degenerate][degenerate-distribution] distribution object has the following properties and methods... 68 69 ### Writable Properties 70 71 #### degenerate.mu 72 73 Constant value of the distribution. 74 75 ```javascript 76 var degenerate = new Degenerate( 2.0 ); 77 78 var mu = degenerate.mu; 79 // returns 2.0 80 81 degenerate.mu = -2.0; 82 83 mu = degenerate.mu; 84 // returns -2.0 85 ``` 86 87 * * * 88 89 ### Computed Properties 90 91 #### Degenerate.prototype.entropy 92 93 Returns the [differential entropy][entropy]. 94 95 ```javascript 96 var degenerate = new Degenerate( 4.0 ); 97 98 var entropy = degenerate.entropy; 99 // returns 0.0 100 ``` 101 102 #### Degenerate.prototype.mean 103 104 Returns the [mean][expected-value]. 105 106 ```javascript 107 var degenerate = new Degenerate( 10.0 ); 108 109 var mu = degenerate.mean; 110 // returns 10.0 111 ``` 112 113 #### Degenerate.prototype.median 114 115 Returns the [median][median]. 116 117 ```javascript 118 var degenerate = new Degenerate( 10.0 ); 119 120 var median = degenerate.median; 121 // returns 10.0 122 ``` 123 124 #### Degenerate.prototype.mode 125 126 Returns the [mode][mode]. 127 128 ```javascript 129 var degenerate = new Degenerate( 10.0 ); 130 131 var mode = degenerate.mode; 132 // returns 10.0 133 ``` 134 135 #### Degenerate.prototype.stdev 136 137 Returns the [standard deviation][standard-deviation]. 138 139 ```javascript 140 var degenerate = new Degenerate( 4.0 ); 141 142 var s = degenerate.stdev; 143 // returns 0.0 144 ``` 145 146 #### Degenerate.prototype.variance 147 148 Returns the [variance][variance]. 149 150 ```javascript 151 var degenerate = new Degenerate( 4.0 ); 152 153 var s2 = degenerate.variance; 154 // returns 0.0 155 ``` 156 157 * * * 158 159 ### Methods 160 161 #### Degenerate.prototype.cdf( x ) 162 163 Evaluates the [cumulative distribution function][cdf] (CDF). 164 165 ```javascript 166 var degenerate = new Degenerate( 0.2 ); 167 168 var y = degenerate.cdf( 0.5 ); 169 // returns 1.0 170 ``` 171 172 #### Degenerate.prototype.logcdf( x ) 173 174 Evaluates the natural logarithm of the [cumulative distribution function][cdf] (logCDF). 175 176 ```javascript 177 var degenerate = new Degenerate( 0.2 ); 178 179 var y = degenerate.logcdf( 0.5 ); 180 // returns 0.0 181 ``` 182 183 #### Degenerate.prototype.logpdf( x ) 184 185 Evaluates the natural logarithm of the [probability density function][pdf] (logPDF). 186 187 ```javascript 188 var degenerate = new Degenerate( 10.0 ); 189 190 var y = degenerate.logpdf( 9.0 ); 191 // returns -Infinity 192 193 y = degenerate.logpdf( 10.0 ); 194 // returns Infinity 195 ``` 196 197 #### Degenerate.prototype.logpmf( x ) 198 199 Evaluates the natural logarithm of the [probability mass function][pmf] (logPMF). 200 201 ```javascript 202 var degenerate = new Degenerate( 10.0 ); 203 204 var y = degenerate.logpmf( 9.0 ); 205 // returns -Infinity 206 207 y = degenerate.logpmf( 10.0 ); 208 // returns 0.0 209 ``` 210 211 #### Degenerate.prototype.mgf( t ) 212 213 Evaluates the [moment-generating function][mgf] (MGF). 214 215 ```javascript 216 var degenerate = new Degenerate( 10.0 ); 217 218 var y = degenerate.mgf( 0.1 ); 219 // returns ~2.718 220 ``` 221 222 #### Degenerate.prototype.pdf( x ) 223 224 Evaluates the [probability density function][pdf] (PDF). 225 226 ```javascript 227 var degenerate = new Degenerate( 10.0 ); 228 229 var y = degenerate.pdf( 2.0 ); 230 // returns 0.0 231 232 y = degenerate.pdf( 10.0 ); 233 // returns +Infinity 234 ``` 235 236 #### Degenerate.prototype.pmf( x ) 237 238 Evaluates the [probability mass function][pmf] (PMF). 239 240 ```javascript 241 var degenerate = new Degenerate( 10.0 ); 242 243 var y = degenerate.pmf( 2.0 ); 244 // returns 0.0 245 246 y = degenerate.pmf( 10.0 ); 247 // returns 1.0 248 ``` 249 250 #### Degenerate.prototype.quantile( p ) 251 252 Evaluates the [quantile function][quantile-function] at probability `p`. 253 254 ```javascript 255 var degenerate = new Degenerate( 10.0 ); 256 257 var y = degenerate.quantile( 0.5 ); 258 // returns 10.0 259 260 y = degenerate.quantile( 0.9 ); 261 // returns 10.0 262 ``` 263 264 </section> 265 266 <!-- /.usage --> 267 268 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> 269 270 <section class="notes"> 271 272 </section> 273 274 <!-- /.notes --> 275 276 <!-- Package usage examples. --> 277 278 * * * 279 280 <section class="examples"> 281 282 ## Examples 283 284 <!-- eslint no-undef: "error" --> 285 286 ```javascript 287 var Degenerate = require( '@stdlib/stats/base/dists/degenerate/ctor' ); 288 289 var degenerate = new Degenerate( 0.5 ); 290 291 var mu = degenerate.mean; 292 // returns 0.5 293 294 var s2 = degenerate.variance; 295 // returns 0.0 296 297 var y = degenerate.cdf( 2.0 ); 298 // returns 1.0 299 ``` 300 301 </section> 302 303 <!-- /.examples --> 304 305 <!-- 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. --> 306 307 <section class="references"> 308 309 </section> 310 311 <!-- /.references --> 312 313 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> 314 315 <section class="links"> 316 317 [degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution 318 319 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function 320 321 [mgf]: https://en.wikipedia.org/wiki/Moment-generating_function 322 323 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function 324 325 [pmf]: https://en.wikipedia.org/wiki/Probability_mass_function 326 327 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function 328 329 [entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29 330 331 [expected-value]: https://en.wikipedia.org/wiki/Expected_value 332 333 [median]: https://en.wikipedia.org/wiki/Median 334 335 [mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29 336 337 [standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation 338 339 [variance]: https://en.wikipedia.org/wiki/Variance 340 341 </section> 342 343 <!-- /.links -->