README.md (4886B)
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 # incrmmda 22 23 > Compute a moving [mean directional accuracy][mean-directional-accuracy] (MDA) incrementally. 24 25 <section class="intro"> 26 27 For a window of size `W`, the [mean directional accuracy][mean-directional-accuracy] is defined as 28 29 <!-- <equation class="equation" label="eq:mean_directional_accuracy" align="center" raw="\operatorname{MDA} = \begin{cases} 1 & \textrm{if}\ W = 1 \\ \frac{1}{W} \sum_{i=1}^{W} \delta_{\operatorname{sgn}(\Delta f_{i,i-1}),\ \operatorname{sgn}(\Delta a_{i,i-1})} & \textrm{if}\ W > 1 \end{cases}" alt="Equation for the mean directional accuracy."> --> 30 31 <div class="equation" align="center" data-raw-text="\operatorname{MDA} = \begin{cases} 1 & \textrm{if}\ W = 1 \\\frac{1}{W} \sum_{i=1}^{W} \delta_{\operatorname{sgn}(\Delta f_{i,i-1}),\ \operatorname{sgn}(\Delta a_{i,i-1})} & \textrm{if}\ W > 1 \end{cases}" data-equation="eq:mean_directional_accuracy"> 32 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@99730afbace8256ce53cfbc0714c7f3cac92466a/lib/node_modules/@stdlib/stats/incr/mmda/docs/img/equation_mean_directional_accuracy.svg" alt="Equation for the mean directional accuracy."> 33 <br> 34 </div> 35 36 <!-- </equation> --> 37 38 where `f_i` is the forecast value, `a_i` is the actual value, `sgn(x)` is the [signum][@stdlib/math/base/special/signum] function, and `δ` is the [Kronecker delta][@stdlib/math/base/special/kronecker-delta]. 39 40 </section> 41 42 <!-- /.intro --> 43 44 <section class="usage"> 45 46 ## Usage 47 48 ```javascript 49 var incrmmda = require( '@stdlib/stats/incr/mmda' ); 50 ``` 51 52 #### incrmmda( window ) 53 54 Returns an accumulator `function` which incrementally computes a moving [mean directional accuracy][mean-directional-accuracy]. The `window` parameter defines the number of values over which to compute the moving [mean directional accuracy][mean-directional-accuracy]. 55 56 ```javascript 57 var accumulator = incrmmda( 3 ); 58 ``` 59 60 #### accumulator( \[f, a] ) 61 62 If provided input values `f` and `a`, the accumulator function returns an updated [mean directional accuracy][mean-directional-accuracy]. If not provided input values `f` and `a`, the accumulator function returns the current [mean directional accuracy][mean-directional-accuracy]. 63 64 ```javascript 65 var accumulator = incrmmda( 3 ); 66 67 var m = accumulator(); 68 // returns null 69 70 // Fill the window... 71 m = accumulator( 2.0, 3.0 ); // [(+,+)] 72 // returns 1.0 73 74 m = accumulator( 1.0, 4.0 ); // [(+,+), (-,+)] 75 // returns 0.5 76 77 m = accumulator( 3.0, 9.0 ); // [(+,+), (-,+), (+,+)] 78 // returns ~0.67 79 80 // Window begins sliding... 81 m = accumulator( 7.0, 3.0 ); // [(-,+), (+,+), (+,-)] 82 // returns ~0.33 83 84 m = accumulator( 5.0, 3.0 ); // [(+,+), (+,-), (-,0)] 85 // returns ~0.33 86 87 m = accumulator(); 88 // returns ~0.33 89 ``` 90 91 </section> 92 93 <!-- /.usage --> 94 95 <section class="notes"> 96 97 ## Notes 98 99 - 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 **at least** `W-1` 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. 100 - As `W` (f,a) pairs are needed to fill the window buffer, the first `W-1` returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values. 101 102 </section> 103 104 <!-- /.notes --> 105 106 <section class="examples"> 107 108 ## Examples 109 110 <!-- eslint no-undef: "error" --> 111 112 ```javascript 113 var randu = require( '@stdlib/random/base/randu' ); 114 var incrmmda = require( '@stdlib/stats/incr/mmda' ); 115 116 var accumulator; 117 var v1; 118 var v2; 119 var i; 120 121 // Initialize an accumulator: 122 accumulator = incrmmda( 5 ); 123 124 // For each simulated datum, update the moving mean directional accuracy... 125 for ( i = 0; i < 100; i++ ) { 126 v1 = ( randu()*100.0 ) - 50.0; 127 v2 = ( randu()*100.0 ) - 50.0; 128 accumulator( v1, v2 ); 129 } 130 console.log( accumulator() ); 131 ``` 132 133 </section> 134 135 <!-- /.examples --> 136 137 <section class="links"> 138 139 [mean-directional-accuracy]: https://en.wikipedia.org/wiki/Mean_Directional_Accuracy_%28MDA%29 140 141 [@stdlib/math/base/special/signum]: https://www.npmjs.com/package/@stdlib/math-base-special-signum 142 143 [@stdlib/math/base/special/kronecker-delta]: https://www.npmjs.com/package/@stdlib/math-base-special-kronecker-delta 144 145 </section> 146 147 <!-- /.links -->