README.md (6659B)
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 # Kolmogorov-Smirnov Goodness-of-Fit Test 22 23 > One-sample Kolmogorov-Smirnov goodness-of-fit test. 24 25 <section class="usage"> 26 27 ## Usage 28 29 ```javascript 30 var kstest = require( '@stdlib/stats/kstest' ); 31 ``` 32 33 #### kstest( x, y\[, ...params]\[, opts] ) 34 35 For a numeric [array][mdn-array] or [typed array][mdn-typed-array] 36 `x`, a Kolmogorov-Smirnov goodness-of-fit is computed for the null hypothesis that the values of `x` come from the distribution specified by `y`. `y` can be either a [string][mdn-string] with the name of the distribution to test against, or a [function][mdn-function]. In the latter case, `y` is expected to be the cumulative distribution function (CDF) of the distribution to test against, with its first parameter being the value at which to evaluate the CDF and the remaining parameters constituting the parameters of the distribution. The parameters of the distribution are passed as additional arguments after `y` from `kstest` to the chosen CDF. The function returns an object holding the calculated test statistic `statistic` and the `pValue` of the test. 37 38 ```javascript 39 var factory = require( '@stdlib/random/base/uniform' ).factory; 40 var runif; 41 var out; 42 var x; 43 var i; 44 45 runif = factory( 0.0, 1.0, { 46 'seed': 8798 47 }); 48 49 x = new Array( 100 ); 50 for ( i = 0; i < x.length; i++ ) { 51 x[ i ] = runif(); 52 } 53 out = kstest( x, 'uniform', 0.0, 1.0 ); 54 // returns { 'pValue': ~0.703, 'statistic': ~0.069, ... } 55 ``` 56 57 The returned object comes with a `.print()` method which when invoked will print a formatted output of the hypothesis test results. `print` accepts a `digits` option that controls the number of decimal digits displayed for the outputs and a `decision` option, which when set to `false` will hide the test decision. 58 59 <!-- run-disable --> 60 61 ```javascript 62 console.log( out.print() ); 63 /* e.g., => 64 Kolmogorov-Smirnov goodness-of-fit test. 65 66 Null hypothesis: the CDF of `x` is equal equal to the reference CDF. 67 68 pValue: 0.7039 69 statistic: 0.0689 70 71 Test Decision: Fail to reject null in favor of alternative at 5% significance level 72 */ 73 ``` 74 75 The function accepts the following `options`: 76 77 - **alpha**: `number` in the interval `[0,1]` giving the significance level of the hypothesis test. Default: `0.05`. 78 - **alternative**: Either `two-sided`, `less` or `greater`. Indicates whether the alternative hypothesis is that the true distribution of `x` is not equal to the reference distribution specified by `y` (`two-sided`), whether it is `less` than the reference distribution or `greater` than the reference distribution. Default: `two-sided`. 79 - **sorted**: `boolean` indicating if the `x` [array][mdn-array] is in sorted order (ascending). Default: `false`. 80 81 By default, the test is carried out at a significance level of `0.05`. To choose a custom significance level, set the `alpha` option. 82 83 <!-- run-disable --> 84 85 ```javascript 86 out = kstest( x, 'uniform', 0.0, 1.0, { 87 'alpha': 0.1 88 }); 89 console.log( out.print() ); 90 /* e.g., => 91 Kolmogorov-Smirnov goodness-of-fit test. 92 93 Null hypothesis: the CDF of `x` is equal equal to the reference CDF. 94 95 pValue: 0.7039 96 statistic: 0.0689 97 98 Test Decision: Fail to reject null in favor of alternative at 10% significance level 99 */ 100 ``` 101 102 By default, the function tests the null hypothesis that the true distribution of `x` and the reference distribution `y` are equal to each other against the alternative that they are not equal. To carry out a one-sided hypothesis test, set the `alternative` option to either `less` or `greater`. 103 104 ```javascript 105 var factory = require( '@stdlib/random/base/uniform' ).factory; 106 var runif; 107 var out; 108 var x; 109 var i; 110 111 runif = factory( 0.0, 1.0, { 112 'seed': 8798 113 }); 114 115 x = new Array( 100 ); 116 for ( i = 0; i < x.length; i++ ) { 117 x[ i ] = runif(); 118 } 119 120 out = kstest( x, 'uniform', 0.0, 1.0, { 121 'alternative': 'less' 122 }); 123 // returns { 'pValue': ~0.358, 'statistic': ~0.07, ... } 124 125 out = kstest( x, 'uniform', 0.0, 1.0, { 126 'alternative': 'greater' 127 }); 128 // returns { 'pValue': ~0.907, 'statistic': ~0.02, ... } 129 ``` 130 131 To perform the Kolmogorov-Smirnov test, the data has to be sorted in ascending order. If the data in `x` are already sorted, set the `sorted` option to `true` to speed up computation. 132 133 ```javascript 134 x = [ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 ]; 135 136 out = kstest( x, 'uniform', 0.0, 1.0, { 137 'sorted': true 138 }); 139 // returns { 'pValue': ~1, 'statistic': 0.1, ... } 140 ``` 141 142 </section> 143 144 <!-- /.usage --> 145 146 <section class="examples"> 147 148 ## Examples 149 150 <!-- eslint no-undef: "error" --> 151 152 ```javascript 153 var kstest = require( '@stdlib/stats/kstest' ); 154 var factory = require( '@stdlib/random/base/normal' ).factory; 155 156 var rnorm; 157 var table; 158 var out; 159 var i; 160 var x; 161 162 rnorm = factory({ 163 'seed': 4839 164 }); 165 166 // Values drawn from a Normal(3,1) distribution 167 x = new Array( 100 ); 168 for ( i = 0; i < 100; i++ ) { 169 x[ i ] = rnorm( 3.0, 1.0 ); 170 } 171 172 // Test against N(0,1) 173 out = kstest( x, 'normal', 0.0, 1.0 ); 174 table = out.print(); 175 /* e.g., returns 176 Kolmogorov-Smirnov goodness-of-fit test. 177 178 Null hypothesis: the CDF of `x` is equal to the reference CDF. 179 180 statistic: 0.847 181 pValue: 0 182 183 Test Decision: Reject null in favor of alternative at 5% significance level 184 */ 185 186 // Test against N(3,1) 187 out = kstest( x, 'normal', 3.0, 1.0 ); 188 table = out.print(); 189 /* e.g., returns 190 Kolmogorov-Smirnov goodness-of-fit test. 191 192 Null hypothesis: the CDF of `x` is equal to the reference CDF. 193 194 statistic: 0.0733 195 pValue: 0.6282 196 197 Test Decision: Fail to reject null in favor of alternative at 5% significance level 198 */ 199 ``` 200 201 </section> 202 203 <!-- /.examples --> 204 205 <section class="links"> 206 207 [mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array 208 209 [mdn-function]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Function 210 211 [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays 212 213 [mdn-string]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/String 214 215 </section> 216 217 <!-- /.links -->