README.md (5467B)
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 # incrcv 22 23 > Compute the [coefficient of variation][coefficient-of-variation] (CV) incrementally. 24 25 <section class="intro"> 26 27 The [corrected sample standard deviation][sample-stdev] is defined as 28 29 <!-- <equation class="equation" label="eq:corrected_sample_standard_deviation" align="center" raw="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2}" alt="Equation for the corrected sample standard deviation."> --> 30 31 <div class="equation" align="center" data-raw-text="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2}" data-equation="eq:corrected_sample_standard_deviation"> 32 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@6dd7df93fd2c6e40fd0662844acf8b69b887dcec/lib/node_modules/@stdlib/stats/incr/cv/docs/img/equation_corrected_sample_standard_deviation.svg" alt="Equation for the corrected sample standard deviation."> 33 <br> 34 </div> 35 36 <!-- </equation> --> 37 38 and the [arithmetic mean][arithmetic-mean] is defined as 39 40 <!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> --> 41 42 <div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean"> 43 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@6dd7df93fd2c6e40fd0662844acf8b69b887dcec/lib/node_modules/@stdlib/stats/incr/cv/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean."> 44 <br> 45 </div> 46 47 <!-- </equation> --> 48 49 The [coefficient of variation][coefficient-of-variation] (also known as **relative standard deviation**, RSD) is defined as 50 51 <!-- <equation class="equation" label="eq:coefficient_of_variation" align="center" raw="c_v = \frac{s}{\bar{x}}" alt="Equation for the coefficient of variation (CV)."> --> 52 53 <div class="equation" align="center" data-raw-text="c_v = \frac{s}{\bar{x}}" data-equation="eq:coefficient_of_variation"> 54 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@6dd7df93fd2c6e40fd0662844acf8b69b887dcec/lib/node_modules/@stdlib/stats/incr/cv/docs/img/equation_coefficient_of_variation.svg" alt="Equation for the coefficient of variation (CV)."> 55 <br> 56 </div> 57 58 <!-- </equation> --> 59 60 </section> 61 62 <!-- /.intro --> 63 64 <section class="usage"> 65 66 ## Usage 67 68 ```javascript 69 var incrcv = require( '@stdlib/stats/incr/cv' ); 70 ``` 71 72 #### incrcv( \[mean] ) 73 74 Returns an accumulator `function` which incrementally computes the [coefficient of variation][coefficient-of-variation]. 75 76 ```javascript 77 var accumulator = incrcv(); 78 ``` 79 80 If the mean is already known, provide a `mean` argument. 81 82 ```javascript 83 var accumulator = incrcv( 3.0 ); 84 ``` 85 86 #### accumulator( \[x] ) 87 88 If provided an input value `x`, the accumulator function returns an updated accumulated value. If not provided an input value `x`, the accumulator function returns the current accumulated value. 89 90 ```javascript 91 var accumulator = incrcv(); 92 93 var cv = accumulator( 2.0 ); 94 // returns 0.0 95 96 cv = accumulator( 1.0 ); // => s^2 = ((2-1.5)^2+(1-1.5)^2) / (2-1) 97 // returns ~0.47 98 99 cv = accumulator( 3.0 ); // => s^2 = ((2-2)^2+(1-2)^2+(3-2)^2) / (3-1) 100 // returns 0.5 101 102 cv = accumulator(); 103 // returns 0.5 104 ``` 105 106 </section> 107 108 <!-- /.usage --> 109 110 <section class="notes"> 111 112 ## Notes 113 114 - Input values are **not** type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, the accumulated value is `NaN` for **all** future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function. 115 - The [coefficient of variation][coefficient-of-variation] is typically computed on nonnegative values. The measure may lack meaning for data which can assume both positive and negative values. 116 - For small and moderately sized samples, the accumulated value tends to be too low and is thus a **biased** estimator. Provided the generating distribution is known (e.g., a normal distribution), you may want to adjust the accumulated value or use an alternative implementation providing an unbiased estimator. 117 118 </section> 119 120 <!-- /.notes --> 121 122 <section class="examples"> 123 124 ## Examples 125 126 <!-- eslint no-undef: "error" --> 127 128 ```javascript 129 var randu = require( '@stdlib/random/base/randu' ); 130 var incrcv = require( '@stdlib/stats/incr/cv' ); 131 132 var accumulator; 133 var v; 134 var i; 135 136 // Initialize an accumulator: 137 accumulator = incrcv(); 138 139 // For each simulated datum, update the coefficient of variation... 140 for ( i = 0; i < 100; i++ ) { 141 v = randu() * 100.0; 142 accumulator( v ); 143 } 144 console.log( accumulator() ); 145 ``` 146 147 </section> 148 149 <!-- /.examples --> 150 151 <section class="links"> 152 153 [coefficient-of-variation]: https://en.wikipedia.org/wiki/Coefficient_of_variation 154 155 [arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean 156 157 [sample-stdev]: https://en.wikipedia.org/wiki/Standard_deviation 158 159 </section> 160 161 <!-- /.links -->