README.md (6335B)
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 # Uniform 22 23 > Uniform 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 Uniform = require( '@stdlib/stats/base/dists/uniform/ctor' ); 41 ``` 42 43 #### Uniform( \[a, b] ) 44 45 Returns an [uniform][uniform-distribution] distribution object. 46 47 ```javascript 48 var uniform = new Uniform(); 49 50 var mu = uniform.mean; 51 // returns 0.5 52 ``` 53 54 By default, `a = 0.0` and `b = 1.0`. To create a distribution having a different `a` (minimum support) and `b` (maximum support), provide the corresponding arguments. 55 56 ```javascript 57 var uniform = new Uniform( 2.0, 4.0 ); 58 59 var mu = uniform.mean; 60 // returns 3.0 61 ``` 62 63 * * * 64 65 ## uniform 66 67 An [uniform][uniform-distribution] distribution object has the following properties and methods... 68 69 ### Writable Properties 70 71 #### uniform.a 72 73 Minimum support of the distribution. `a` **must** be a number smaller than `b`. 74 75 ```javascript 76 var uniform = new Uniform(); 77 78 var a = uniform.a; 79 // returns 0.0 80 81 uniform.a = 0.5; 82 83 a = uniform.a; 84 // returns 0.5 85 ``` 86 87 #### uniform.b 88 89 Maximum support of the distribution. `b` **must** be a number larger than `a`. 90 91 ```javascript 92 var uniform = new Uniform( 2.0, 4.0 ); 93 94 var b = uniform.b; 95 // returns 4.0 96 97 uniform.b = 3.0; 98 99 b = uniform.b; 100 // returns 3.0 101 ``` 102 103 * * * 104 105 ### Computed Properties 106 107 #### Uniform.prototype.entropy 108 109 Returns the [differential entropy][entropy]. 110 111 ```javascript 112 var uniform = new Uniform( 4.0, 12.0 ); 113 114 var entropy = uniform.entropy; 115 // returns ~2.079 116 ``` 117 118 #### Uniform.prototype.kurtosis 119 120 Returns the [excess kurtosis][kurtosis]. 121 122 ```javascript 123 var uniform = new Uniform( 4.0, 12.0 ); 124 125 var kurtosis = uniform.kurtosis; 126 // returns -1.2 127 ``` 128 129 #### Uniform.prototype.mean 130 131 Returns the [expected value][expected-value]. 132 133 ```javascript 134 var uniform = new Uniform( 4.0, 12.0 ); 135 136 var mu = uniform.mean; 137 // returns 8.0 138 ``` 139 140 #### Uniform.prototype.median 141 142 Returns the [median][median]. 143 144 ```javascript 145 var uniform = new Uniform( 4.0, 12.0 ); 146 147 var median = uniform.median; 148 // returns 8.0 149 ``` 150 151 #### Uniform.prototype.skewness 152 153 Returns the [skewness][skewness]. 154 155 ```javascript 156 var uniform = new Uniform( 4.0, 12.0 ); 157 158 var skewness = uniform.skewness; 159 // returns 0.0 160 ``` 161 162 #### Uniform.prototype.stdev 163 164 Returns the [standard deviation][standard-deviation]. 165 166 ```javascript 167 var uniform = new Uniform( 4.0, 12.0 ); 168 169 var s = uniform.stdev; 170 // returns ~2.309 171 ``` 172 173 #### Uniform.prototype.variance 174 175 Returns the [variance][variance]. 176 177 ```javascript 178 var uniform = new Uniform( 4.0, 12.0 ); 179 180 var s2 = uniform.variance; 181 // returns ~5.333 182 ``` 183 184 * * * 185 186 ### Methods 187 188 #### Uniform.prototype.cdf( x ) 189 190 Evaluates the [cumulative distribution function][cdf] (CDF). 191 192 ```javascript 193 var uniform = new Uniform( 2.0, 4.0 ); 194 195 var y = uniform.cdf( 2.5 ); 196 // returns 0.25 197 ``` 198 199 #### Uniform.prototype.logcdf( x ) 200 201 Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF). 202 203 ```javascript 204 var uniform = new Uniform( 2.0, 4.0 ); 205 206 var y = uniform.logcdf( 2.5 ); 207 // returns ~-1.386 208 ``` 209 210 #### Uniform.prototype.logpdf( x ) 211 212 Evaluates the natural logarithm of the [probability density function][pdf] (PDF). 213 214 ```javascript 215 var uniform = new Uniform( 2.0, 4.0 ); 216 217 var y = uniform.logpdf( 2.5 ); 218 // returns ~-0.693 219 ``` 220 221 #### Uniform.prototype.pdf( x ) 222 223 Evaluates the [probability density function][pdf] (PDF). 224 225 ```javascript 226 var uniform = new Uniform( 2.0, 4.0 ); 227 228 var y = uniform.pdf( 2.5 ); 229 // returns 0.5 230 ``` 231 232 #### Uniform.prototype.quantile( p ) 233 234 Evaluates the [quantile function][quantile-function] at probability `p`. 235 236 ```javascript 237 var uniform = new Uniform( 2.0, 4.0 ); 238 239 var y = uniform.quantile( 0.5 ); 240 // returns 3.0 241 242 y = uniform.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 Uniform = require( '@stdlib/stats/base/dists/uniform/ctor' ); 270 271 var uniform = new Uniform( 2.0, 4.0 ); 272 273 var mu = uniform.mean; 274 // returns 3.0 275 276 var median = uniform.median; 277 // returns 3.0 278 279 var s2 = uniform.variance; 280 // returns ~0.333 281 282 var y = uniform.cdf( 2.5 ); 283 // returns 0.25 284 ``` 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 [uniform-distribution]: https://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29 303 304 [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 [skewness]: https://en.wikipedia.org/wiki/Skewness 319 320 [standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation 321 322 [variance]: https://en.wikipedia.org/wiki/Variance 323 324 </section> 325 326 <!-- /.links -->