README.md (6134B)
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 # ChiSquare 22 23 > Chi-squared 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 ChiSquare = require( '@stdlib/stats/base/dists/chisquare/ctor' ); 41 ``` 42 43 #### ChiSquare( \[k] ) 44 45 Returns an [chi-squared][chisquare-distribution] distribution object. 46 47 ```javascript 48 var chisquare = new ChiSquare(); 49 50 var mu = chisquare.mean; 51 // returns 1.0 52 ``` 53 54 By default, `k = 1.0`. To create a distribution having a different degrees of freedom `k`, provide a parameter value. 55 56 ```javascript 57 var chisquare = new ChiSquare( 4.0 ); 58 59 var mu = chisquare.mean; 60 // returns 4.0 61 ``` 62 63 * * * 64 65 ## chisquare 66 67 A [chi-squared][chisquare-distribution] distribution object has the following properties and methods... 68 69 ### Writable Properties 70 71 #### chisquare.k 72 73 Rate parameter of the distribution. `k` **must** be a positive number. 74 75 ```javascript 76 var chisquare = new ChiSquare( 2.0 ); 77 78 var k = chisquare.k; 79 // returns 2.0 80 81 chisquare.k = 3.0; 82 83 k = chisquare.k; 84 // returns 3.0 85 ``` 86 87 * * * 88 89 ### Computed Properties 90 91 #### ChiSquare.prototype.entropy 92 93 Returns the [differential entropy][entropy]. 94 95 ```javascript 96 var chisquare = new ChiSquare( 4.0 ); 97 98 var entropy = chisquare.entropy; 99 // returns ~2.27 100 ``` 101 102 #### ChiSquare.prototype.kurtosis 103 104 Returns the [excess kurtosis][kurtosis]. 105 106 ```javascript 107 var chisquare = new ChiSquare( 4.0 ); 108 109 var kurtosis = chisquare.kurtosis; 110 // returns 3.0 111 ``` 112 113 #### ChiSquare.prototype.mean 114 115 Returns the [expected value][expected-value]. 116 117 ```javascript 118 var chisquare = new ChiSquare( 4.0 ); 119 120 var mu = chisquare.mean; 121 // returns 4.0 122 ``` 123 124 #### ChiSquare.prototype.median 125 126 Returns the [median][median]. 127 128 ```javascript 129 var chisquare = new ChiSquare( 4.0 ); 130 131 var median = chisquare.median; 132 // returns ~3.357 133 ``` 134 135 #### ChiSquare.prototype.mode 136 137 Returns the [mode][mode]. 138 139 ```javascript 140 var chisquare = new ChiSquare( 4.0 ); 141 142 var mode = chisquare.mode; 143 // returns 2.0 144 ``` 145 146 #### ChiSquare.prototype.skewness 147 148 Returns the [skewness][skewness]. 149 150 ```javascript 151 var chisquare = new ChiSquare( 4.0 ); 152 153 var skewness = chisquare.skewness; 154 // returns ~1.414 155 ``` 156 157 #### ChiSquare.prototype.stdev 158 159 Returns the [standard deviation][standard-deviation]. 160 161 ```javascript 162 var chisquare = new ChiSquare( 4.0 ); 163 164 var s = chisquare.stdev; 165 // returns ~2.828 166 ``` 167 168 #### ChiSquare.prototype.variance 169 170 Returns the [variance][variance]. 171 172 ```javascript 173 var chisquare = new ChiSquare( 4.0 ); 174 175 var s2 = chisquare.variance; 176 // returns 8.0 177 ``` 178 179 * * * 180 181 ### Methods 182 183 #### ChiSquare.prototype.cdf( x ) 184 185 Evaluates the [cumulative distribution function][cdf] (CDF). 186 187 ```javascript 188 var chisquare = new ChiSquare( 2.0 ); 189 190 var y = chisquare.cdf( 0.5 ); 191 // returns ~0.221 192 ``` 193 194 #### ChiSquare.prototype.mgf( t ) 195 196 Evaluates the [moment-generating function][mgf] (MGF). 197 198 ```javascript 199 var chisquare = new ChiSquare( 2.0 ); 200 201 var y = chisquare.mgf( 0.2 ); 202 // returns ~1.667 203 ``` 204 205 #### ChiSquare.prototype.pdf( x ) 206 207 Evaluates the [probability density function][pdf] (PDF). 208 209 ```javascript 210 var chisquare = new ChiSquare( 2.0 ); 211 212 var y = chisquare.pdf( 0.8 ); 213 // returns ~0.335 214 ``` 215 216 #### ChiSquare.prototype.quantile( p ) 217 218 Evaluates the [quantile function][quantile-function] at probability `p`. 219 220 ```javascript 221 var chisquare = new ChiSquare( 2.0 ); 222 223 var y = chisquare.quantile( 0.5 ); 224 // returns ~1.386 225 226 y = chisquare.quantile( 1.9 ); 227 // returns NaN 228 ``` 229 230 </section> 231 232 <!-- /.usage --> 233 234 <!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> 235 236 <section class="notes"> 237 238 </section> 239 240 <!-- /.notes --> 241 242 <!-- Package usage examples. --> 243 244 * * * 245 246 <section class="examples"> 247 248 ## Examples 249 250 <!-- eslint no-undef: "error" --> 251 252 ```javascript 253 var ChiSquare = require( '@stdlib/stats/base/dists/chisquare/ctor' ); 254 255 var chisquare = new ChiSquare( 2.0 ); 256 257 var mu = chisquare.mean; 258 // returns 2.0 259 260 var mode = chisquare.mode; 261 // returns 0.0 262 263 var s2 = chisquare.variance; 264 // returns 4.0 265 266 var y = chisquare.cdf( 0.8 ); 267 // returns ~0.33 268 ``` 269 270 </section> 271 272 <!-- /.examples --> 273 274 <!-- 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. --> 275 276 <section class="references"> 277 278 </section> 279 280 <!-- /.references --> 281 282 <!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> 283 284 <section class="links"> 285 286 [chisquare-distribution]: https://en.wikipedia.org/wiki/Chi-squared_distribution 287 288 [cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function 289 290 [mgf]: https://en.wikipedia.org/wiki/Moment-generating_function 291 292 [pdf]: https://en.wikipedia.org/wiki/Probability_density_function 293 294 [quantile-function]: https://en.wikipedia.org/wiki/Quantile_function 295 296 [entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29 297 298 [expected-value]: https://en.wikipedia.org/wiki/Expected_value 299 300 [kurtosis]: https://en.wikipedia.org/wiki/Kurtosis 301 302 [median]: https://en.wikipedia.org/wiki/Median 303 304 [mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29 305 306 [skewness]: https://en.wikipedia.org/wiki/Skewness 307 308 [standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation 309 310 [variance]: https://en.wikipedia.org/wiki/Variance 311 312 </section> 313 314 <!-- /.links -->