README.md (6302B)
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 # Poisson 22 23 > Poisson 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 Poisson = require( '@stdlib/stats/base/dists/poisson/ctor' ); 41 ``` 42 43 #### Poisson( \[lambda] ) 44 45 Returns an [Poisson][poisson-distribution] distribution object. 46 47 ```javascript 48 var poisson = new Poisson(); 49 50 var lambda = poisson.mean; 51 // returns 1.0 52 ``` 53 54 By default, `lambda = 1.0`. To create a distribution having a different mean parameter `lambda`, provide a parameter value. 55 56 ```javascript 57 var poisson = new Poisson( 4.0 ); 58 59 var lambda = poisson.mean; 60 // returns 4.0 61 ``` 62 63 * * * 64 65 ## poisson 66 67 A [Poisson][poisson-distribution] distribution object has the following properties and methods... 68 69 ### Writable Properties 70 71 #### poisson.lambda 72 73 Mean parameter of the distribution. `lambda` **must** be a positive number. 74 75 ```javascript 76 var poisson = new Poisson( 2.0 ); 77 78 var lambda = poisson.lambda; 79 // returns 2.0 80 81 poisson.lambda = 3.0; 82 83 lambda = poisson.lambda; 84 // returns 3.0 85 ``` 86 87 * * * 88 89 ### Computed Properties 90 91 #### Poisson.prototype.entropy 92 93 Returns the [differential entropy][entropy]. 94 95 ```javascript 96 var poisson = new Poisson( 4.0 ); 97 98 var entropy = poisson.entropy; 99 // returns ~2.087 100 ``` 101 102 #### Poisson.prototype.kurtosis 103 104 Returns the [excess kurtosis][kurtosis]. 105 106 ```javascript 107 var poisson = new Poisson( 4.0 ); 108 109 var kurtosis = poisson.kurtosis; 110 // returns 0.25 111 ``` 112 113 #### Poisson.prototype.mean 114 115 Returns the [median][expected-value]. 116 117 ```javascript 118 var poisson = new Poisson( 4.0 ); 119 120 var mu = poisson.mean; 121 // returns 4.0 122 ``` 123 124 #### Poisson.prototype.median 125 126 Returns the [median][median]. 127 128 ```javascript 129 var poisson = new Poisson( 4.0 ); 130 131 var median = poisson.median; 132 // returns 4.0 133 ``` 134 135 #### Poisson.prototype.mode 136 137 Returns the [mode][mode]. 138 139 ```javascript 140 var poisson = new Poisson( 4.0 ); 141 142 var mode = poisson.mode; 143 // returns 4.0 144 ``` 145 146 #### Poisson.prototype.skewness 147 148 Returns the [skewness][skewness]. 149 150 ```javascript 151 var poisson = new Poisson( 4.0 ); 152 153 var skewness = poisson.skewness; 154 // returns 0.5 155 ``` 156 157 #### Poisson.prototype.stdev 158 159 Returns the [standard deviation][standard-deviation]. 160 161 ```javascript 162 var poisson = new Poisson( 4.0 ); 163 164 var s = poisson.stdev; 165 // returns 2.0 166 ``` 167 168 #### Poisson.prototype.variance 169 170 Returns the [variance][variance]. 171 172 ```javascript 173 var poisson = new Poisson( 4.0 ); 174 175 var s2 = poisson.variance; 176 // returns 4.0 177 ``` 178 179 * * * 180 181 ### Methods 182 183 #### Poisson.prototype.cdf( x ) 184 185 Evaluates the [cumulative distribution function][cdf] (CDF). 186 187 ```javascript 188 var poisson = new Poisson( 2.0 ); 189 190 var y = poisson.cdf( 0.5 ); 191 // returns ~0.135 192 ``` 193 194 #### Poisson.prototype.logpmf( x ) 195 196 Evaluates the natural logarithm of the [probability mass function][pmf] (PMF). 197 198 ```javascript 199 var poisson = new Poisson( 2.0 ); 200 201 var y = poisson.logpmf( 3.0 ); 202 // returns ~-1.712 203 204 y = poisson.logpmf( 2.3 ); 205 // returns -Infinity 206 ``` 207 208 #### Poisson.prototype.mgf( t ) 209 210 Evaluates the [moment-generating function][mgf] (MGF). 211 212 ```javascript 213 var poisson = new Poisson( 2.0 ); 214 215 var y = poisson.mgf( 0.5 ); 216 // returns ~3.66 217 ``` 218 219 #### Poisson.prototype.pmf( x ) 220 221 Evaluates the [probability mass function][pmf] (PMF). 222 223 ```javascript 224 var poisson = new Poisson( 2.0 ); 225 226 var y = poisson.pmf( 3.0 ); 227 // returns ~0.18 228 229 y = poisson.pmf( 2.3 ); 230 // returns 0.0 231 ``` 232 233 #### Poisson.prototype.quantile( p ) 234 235 Evaluates the [quantile function][quantile-function] at probability `p`. 236 237 ```javascript 238 var poisson = new Poisson( 2.0 ); 239 240 var y = poisson.quantile( 0.5 ); 241 // returns 2.0 242 243 y = poisson.quantile( 1.9 ); 244 // returns NaN 245 ``` 246 247 </section> 248 249 <!-- /.usage --> 250 251 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> 252 253 <section class="notes"> 254 255 </section> 256 257 <!-- /.notes --> 258 259 <!-- Package usage examples. --> 260 261 * * * 262 263 <section class="examples"> 264 265 ## Examples 266 267 <!-- eslint no-undef: "error" --> 268 269 ```javascript 270 var Poisson = require( '@stdlib/stats/base/dists/poisson/ctor' ); 271 272 var poisson = new Poisson( 2.0 ); 273 274 var mu = poisson.mean; 275 // returns 2.0 276 277 var mode = poisson.mode; 278 // returns 2.0 279 280 var s2 = poisson.variance; 281 // returns 2.0 282 283 var y = poisson.cdf( 0.8 ); 284 // returns ~0.135 285 ``` 286 287 </section> 288 289 <!-- /.examples --> 290 291 <!-- 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. --> 292 293 <section class="references"> 294 295 </section> 296 297 <!-- /.references --> 298 299 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> 300 301 <section class="links"> 302 303 [poisson-distribution]: https://en.wikipedia.org/wiki/Poisson_distribution 304 305 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function 306 307 [mgf]: https://en.wikipedia.org/wiki/Moment-generating_function 308 309 [pmf]: https://en.wikipedia.org/wiki/Probability_mass_function 310 311 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function 312 313 [entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29 314 315 [expected-value]: https://en.wikipedia.org/wiki/Expected_value 316 317 [kurtosis]: https://en.wikipedia.org/wiki/Kurtosis 318 319 [median]: https://en.wikipedia.org/wiki/Median 320 321 [mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29 322 323 [skewness]: https://en.wikipedia.org/wiki/Skewness 324 325 [standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation 326 327 [variance]: https://en.wikipedia.org/wiki/Variance 328 329 </section> 330 331 <!-- /.links -->