[RFC]: add stats/incr/nanvmr

lib/node_modules/@stdlib/stats/incr/nanvmr/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2018 The Stdlib Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+-->
+
+# incrnanvmr
+
+> Compute a [variance-to-mean ratio][variance-to-mean-ratio] (VMR) incrementally.
+
+<section class="intro">
+
+The [unbiased sample variance][sample-variance] is defined as
+
+<!-- <equation class="equation" label="eq:unbiased_sample_variance" align="center" raw="s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2" alt="Equation for the unbiased sample variance."> -->
+
+```math
+s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2
+```
+
+<!-- <div class="equation" align="center" data-raw-text="s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} ( x_i - \bar{x} )^2" data-equation="eq:unbiased_sample_variance">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@7fe559e94716008fb414ec7c6b3d0e3e1194f2ba/lib/node_modules/@stdlib/stats/incr/vmr/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}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> -->
+
+```math
+\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i
+```
+
+<!-- <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">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@86f8c49b0e95ee794f0b098b8d17444c0cbeea0a/lib/node_modules/@stdlib/stats/incr/vmr/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="D = \frac{s^2}{\bar{x}}" alt="Equation for the variance-to-mean ratio (VMR)."> -->
+
+```math
+D = \frac{s^2}{\bar{x}}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="D = \frac{s^2}{\bar{x}}" data-equation="eq:variance_to_mean_ratio">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@86f8c49b0e95ee794f0b098b8d17444c0cbeea0a/lib/node_modules/@stdlib/stats/incr/vmr/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 incrnanvmr = require( '@stdlib/stats/incr/nanvmr' );
+```
+
+#### incrnanvmr( \[mean] )
+
+Returns an accumulator `function` which incrementally computes a [variance-to-mean ratio][variance-to-mean-ratio], ignoring `NaN` values.
+
+```javascript
+var accumulator = incrnanvmr();
+```
+
+If the mean is already known, provide a `mean` argument.
+
+```javascript
+var accumulator = incrnanvmr( 3.0 );
+```
+
+#### 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 = incrnanvmr();
+
+var D = accumulator( 2.0 );
+// returns 0.0
+
+D = accumulator( 1.0 ); // => s^2 = ((2-1.5)^2+(1-1.5)^2) / (2-1)
+// returns ~0.33
+
+D = accumulator( NaN ); 
+// returns ~0.33
+
+D = accumulator( 3.0 ); // => s^2 = ((2-2)^2+(1-2)^2+(3-2)^2) / (3-1)
+// returns 0.5
+
+D = accumulator();
+// returns 0.5
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Input values are **not** type checked. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.
+
+-   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**, and **relative variance**.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var randu = require( '@stdlib/random/base/randu' );
+var incrnanvmr = require( '@stdlib/stats/incr/nanvmr' );
+
+var accumulator;
+var v;
+var i;
+
+// Initialize an accumulator:
+accumulator = incrnanvmr();
+
+// For each simulated datum, update the variance-to-mean ratio...
+for ( i = 0; i < 100; i++ ) {
+    if ( randu() < 0.2 ) {
+        v = NaN;
+    } else {
+        v = randu() * 100.0;
+    }
+    accumulator( v );
+}
+console.log( accumulator() );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+* * *
+
+## See Also
+
+-   <span class="package-name">[`@stdlib/stats/incr/mean`][@stdlib/stats/incr/mean]</span><span class="delimiter">: </span><span class="description">compute an arithmetic mean incrementally.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/mvmr`][@stdlib/stats/incr/mvmr]</span><span class="delimiter">: </span><span class="description">compute a moving variance-to-mean ratio (VMR) incrementally.</span>
+-   <span class="package-name">[`@stdlib/stats/incr/variance`][@stdlib/stats/incr/variance]</span><span class="delimiter">: </span><span class="description">compute an unbiased sample variance incrementally.</span>
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<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
+
+<!-- <related-links> -->
+
+[@stdlib/stats/incr/mean]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mean
+
+[@stdlib/stats/incr/mvmr]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mvmr
+
+[@stdlib/stats/incr/variance]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/variance
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/incr/nanvmr/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2018 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/base/randu' );
+var pkg = require( './../package.json' ).name;
+var incrnanvmr = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var f;
+	var i;
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		f = incrnanvmr();
+		if ( typeof f !== 'function' ) {
+			b.fail( 'should return a function' );
+		}
+	}
+	b.toc();
+	if ( typeof f !== 'function' ) {
+		b.fail( 'should return a function' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+'::accumulator', function benchmark( b ) {
+	var acc;
+	var v;
+	var i;
+
+	acc = incrnanvmr();
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = acc( randu() );
+		if ( v !== v ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( v !== v ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
+
+bench( pkg+'::accumulator,known_mean', function benchmark( b ) {
+	var acc;
+	var v;
+	var i;
+
+	acc = incrnanvmr( 3.14 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = acc( randu() );
+		if ( v !== v ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( v !== v ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});