time-to-botec

README.md (6835B)

---

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 # incrmvmr
 
 > Compute a moving [variance-to-mean ratio][variance-to-mean-ratio] (VMR) incrementally.
 
 <section class="intro">
 
 For a window of size `W`, the [unbiased sample variance][sample-variance] is defined as
 
 <!-- <equation class="equation" label="eq:unbiased_sample_variance" align="center" raw="s^2 = \frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2" alt="Equation for the unbiased sample variance."> -->
 
 <div class="equation" align="center" data-raw-text="s^2 = \frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2" data-equation="eq:unbiased_sample_variance">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@b331e5634fe726ff0e16e87814ac3f85d8164d31/lib/node_modules/@stdlib/stats/incr/mvmr/docs/img/equation_unbiased_sample_variance.svg" alt="Equation for the unbiased sample variance.">
     <br>
 </div>
 
 <!-- </equation> -->
 
 and the [arithmetic mean][arithmetic-mean] is defined as
 
 <!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\bar{x} = \frac{1}{W} \sum_{i=0}^{W-1} x_i" alt="Equation for the arithmetic mean."> -->
 
 <div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{W} \sum_{i=0}^{W-1} x_i" data-equation="eq:arithmetic_mean">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@164b8f1010c4535340eed9ad0b2af32c4a19863c/lib/node_modules/@stdlib/stats/incr/mvmr/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
     <br>
 </div>
 
 <!-- </equation> -->
 
 The [variance-to-mean ratio][variance-to-mean-ratio] (VMR) is thus defined as
 
 <!-- <equation class="equation" label="eq:variance_to_mean_ratio" align="center" raw="F = \frac{s^2}{\bar{x}}" alt="Equation for the variance-to-mean ratio (VMR)."> -->
 
 <div class="equation" align="center" data-raw-text="F = \frac{s^2}{\bar{x}}" data-equation="eq:variance_to_mean_ratio">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@b331e5634fe726ff0e16e87814ac3f85d8164d31/lib/node_modules/@stdlib/stats/incr/mvmr/docs/img/equation_variance_to_mean_ratio.svg" alt="Equation for the variance-to-mean ratio (VMR).">
     <br>
 </div>
 
 <!-- </equation> -->
 
 </section>
 
 <!-- /.intro -->
 
 <section class="usage">
 
 ## Usage
 
 ```javascript
 var incrmvmr = require( '@stdlib/stats/incr/mvmr' );
 ```
 
 #### incrmvmr( window\[, mean] )
 
 Returns an accumulator `function` which incrementally computes a moving [variance-to-mean ratio][variance-to-mean-ratio]. The `window` parameter defines the number of values over which to compute the moving [variance-to-mean ratio][variance-to-mean-ratio].
 
 ```javascript
 var accumulator = incrmvmr( 3 );
 ```
 
 If the mean is already known, provide a `mean` argument.
 
 ```javascript
 var accumulator = incrmvmr( 3, 5.0 );
 ```
 
 #### accumulator( \[x] )
 
 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.
 
 ```javascript
 var accumulator = incrmvmr( 3 );
 
 var F = accumulator();
 // returns null
 
 // Fill the window...
 F = accumulator( 2.0 ); // [2.0]
 // returns 0.0
 
 F = accumulator( 1.0 ); // [2.0, 1.0]
 // returns ~0.33
 
 F = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
 // returns 0.5
 
 // Window begins sliding...
 F = accumulator( 7.0 ); // [1.0, 3.0, 7.0]
 // returns ~2.55
 
 F = accumulator( 5.0 ); // [3.0, 7.0, 5.0]
 // returns ~0.80
 
 F = accumulator();
 // returns ~0.80
 ```
 
 </section>
 
 <!-- /.usage -->
 
 <section class="notes">
 
 ## Notes
 
 -   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.
 
 -   As `W` values 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.
 
 -   The following table summarizes how to interpret the [variance-to-mean ratio][variance-to-mean-ratio]:
 
     |        VMR        |   Description   |     Example Distribution     |
     | :---------------: | :-------------: | :--------------------------: |
     |         0         |  not dispersed  |           constant           |
     | 0 &lt; VMR &lt; 1 | under-dispersed |           binomial           |
     |         1         |        --       |            Poisson           |
     |         >1        |  over-dispersed | geometric, negative-binomial |
 
     Accordingly, one can use the [variance-to-mean ratio][variance-to-mean-ratio] to assess whether observed data can be modeled as a Poisson process. When observed data is "under-dispersed", observed data may be more regular than as would be the case for a Poisson process. When observed data is "over-dispersed", observed data may contain clusters (i.e., clumped, concentrated data).
 
 -   The [variance-to-mean ratio][variance-to-mean-ratio] is typically computed on nonnegative values. The measure may lack meaning for data which can assume both positive and negative values.
 
 -   The [variance-to-mean ratio][variance-to-mean-ratio] is also known as the **index of dispersion**, **dispersion index**, **coefficient of dispersion**, **relative variance**, and the [**Fano factor**][fano-factor].
 
 </section>
 
 <!-- /.notes -->
 
 <section class="examples">
 
 ## Examples
 
 <!-- eslint no-undef: "error" -->
 
 ```javascript
 var randu = require( '@stdlib/random/base/randu' );
 var incrmvmr = require( '@stdlib/stats/incr/mvmr' );
 
 var accumulator;
 var v;
 var i;
 
 // Initialize an accumulator:
 accumulator = incrmvmr( 5 );
 
 // For each simulated datum, update the moving variance-to-mean ratio...
 for ( i = 0; i < 100; i++ ) {
     v = randu() * 100.0;
     accumulator( v );
 }
 console.log( accumulator() );
 ```
 
 </section>
 
 <!-- /.examples -->
 
 <section class="links">
 
 [variance-to-mean-ratio]: https://en.wikipedia.org/wiki/Index_of_dispersion
 
 [arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean
 
 [sample-variance]: https://en.wikipedia.org/wiki/Variance
 
 [fano-factor]: https://en.wikipedia.org/wiki/Fano_factor
 
 </section>
 
 <!-- /.links -->