Skip to content

Commit 3382cd3

Browse files
23f300130423f3001304
committed
Added nanmvmr
1 parent 1e48327 commit 3382cd3

File tree

13 files changed

+1543
-0
lines changed

13 files changed

+1543
-0
lines changed

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

Lines changed: 229 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,229 @@
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+
# incrmvmr
22+
23+
> Compute a moving [variance-to-mean ratio][variance-to-mean-ratio] (VMR) incrementally.
24+
25+
<section class="intro">
26+
27+
For a window of size `W`, the [unbiased sample variance][sample-variance] is defined as
28+
29+
<!-- <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."> -->
30+
31+
```math
32+
s^2 = \frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2
33+
```
34+
35+
<!-- <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">
36+
<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.">
37+
<br>
38+
</div> -->
39+
40+
<!-- </equation> -->
41+
42+
and the [arithmetic mean][arithmetic-mean] is defined as
43+
44+
<!-- <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."> -->
45+
46+
```math
47+
\bar{x} = \frac{1}{W} \sum_{i=0}^{W-1} x_i
48+
```
49+
50+
<!-- <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">
51+
<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.">
52+
<br>
53+
</div> -->
54+
55+
<!-- </equation> -->
56+
57+
The [variance-to-mean ratio][variance-to-mean-ratio] (VMR) is thus defined as
58+
59+
<!-- <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)."> -->
60+
61+
```math
62+
F = \frac{s^2}{\bar{x}}
63+
```
64+
65+
<!-- <div class="equation" align="center" data-raw-text="F = \frac{s^2}{\bar{x}}" data-equation="eq:variance_to_mean_ratio">
66+
<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).">
67+
<br>
68+
</div> -->
69+
70+
<!-- </equation> -->
71+
72+
</section>
73+
74+
<!-- /.intro -->
75+
76+
<section class="usage">
77+
78+
## Usage
79+
80+
```javascript
81+
var incrmvmr = require( '@stdlib/stats/incr/mvmr' );
82+
```
83+
84+
#### incrmvmr( window\[, mean] )
85+
86+
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].
87+
88+
```javascript
89+
var accumulator = incrmvmr( 3 );
90+
```
91+
92+
If the mean is already known, provide a `mean` argument.
93+
94+
```javascript
95+
var accumulator = incrmvmr( 3, 5.0 );
96+
```
97+
98+
#### accumulator( \[x] )
99+
100+
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.
101+
102+
```javascript
103+
var accumulator = incrmvmr( 3 );
104+
105+
var F = accumulator();
106+
// returns null
107+
108+
// Fill the window...
109+
F = accumulator( 2.0 ); // [2.0]
110+
// returns 0.0
111+
112+
F = accumulator( 1.0 ); // [2.0, 1.0]
113+
// returns ~0.33
114+
115+
F = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
116+
// returns 0.5
117+
118+
// Window begins sliding...
119+
F = accumulator( 7.0 ); // [1.0, 3.0, 7.0]
120+
// returns ~2.55
121+
122+
F = accumulator( 5.0 ); // [3.0, 7.0, 5.0]
123+
// returns ~0.80
124+
125+
F = accumulator();
126+
// returns ~0.80
127+
```
128+
129+
</section>
130+
131+
<!-- /.usage -->
132+
133+
<section class="notes">
134+
135+
## Notes
136+
137+
- 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.
138+
139+
- 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.
140+
141+
- The following table summarizes how to interpret the [variance-to-mean ratio][variance-to-mean-ratio]:
142+
143+
| VMR | Description | Example Distribution |
144+
| :---------------: | :-------------: | :--------------------------: |
145+
| 0 | not dispersed | constant |
146+
| 0 &lt; VMR &lt; 1 | under-dispersed | binomial |
147+
| 1 | -- | Poisson |
148+
| >1 | over-dispersed | geometric, negative-binomial |
149+
150+
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).
151+
152+
- 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.
153+
154+
- 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].
155+
156+
</section>
157+
158+
<!-- /.notes -->
159+
160+
<section class="examples">
161+
162+
## Examples
163+
164+
<!-- eslint no-undef: "error" -->
165+
166+
```javascript
167+
var randu = require( '@stdlib/random/base/randu' );
168+
var incrmvmr = require( '@stdlib/stats/incr/mvmr' );
169+
170+
var accumulator;
171+
var v;
172+
var i;
173+
174+
// Initialize an accumulator:
175+
accumulator = incrmvmr( 5 );
176+
177+
// For each simulated datum, update the moving variance-to-mean ratio...
178+
for ( i = 0; i < 100; i++ ) {
179+
v = randu() * 100.0;
180+
accumulator( v );
181+
}
182+
console.log( accumulator() );
183+
```
184+
185+
</section>
186+
187+
<!-- /.examples -->
188+
189+
<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
190+
191+
<section class="related">
192+
193+
* * *
194+
195+
## See Also
196+
197+
- <span class="package-name">[`@stdlib/stats/incr/mmean`][@stdlib/stats/incr/mmean]</span><span class="delimiter">: </span><span class="description">compute a moving arithmetic mean incrementally.</span>
198+
- <span class="package-name">[`@stdlib/stats/incr/mvariance`][@stdlib/stats/incr/mvariance]</span><span class="delimiter">: </span><span class="description">compute a moving unbiased sample variance incrementally.</span>
199+
- <span class="package-name">[`@stdlib/stats/incr/vmr`][@stdlib/stats/incr/vmr]</span><span class="delimiter">: </span><span class="description">compute a variance-to-mean ratio (VMR) incrementally.</span>
200+
201+
</section>
202+
203+
<!-- /.related -->
204+
205+
<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
206+
207+
<section class="links">
208+
209+
[variance-to-mean-ratio]: https://en.wikipedia.org/wiki/Index_of_dispersion
210+
211+
[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean
212+
213+
[sample-variance]: https://en.wikipedia.org/wiki/Variance
214+
215+
[fano-factor]: https://en.wikipedia.org/wiki/Fano_factor
216+
217+
<!-- <related-links> -->
218+
219+
[@stdlib/stats/incr/mmean]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mmean
220+
221+
[@stdlib/stats/incr/mvariance]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/mvariance
222+
223+
[@stdlib/stats/incr/vmr]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/incr/vmr
224+
225+
<!-- </related-links> -->
226+
227+
</section>
228+
229+
<!-- /.links -->

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

Lines changed: 91 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,91 @@
1+
/**
2+
* @license Apache-2.0
3+
*
4+
* Copyright (c) 2018 The Stdlib Authors.
5+
*
6+
* Licensed under the Apache License, Version 2.0 (the "License");
7+
* you may not use this file except in compliance with the License.
8+
* You may obtain a copy of the License at
9+
*
10+
* http://www.apache.org/licenses/LICENSE-2.0
11+
*
12+
* Unless required by applicable law or agreed to in writing, software
13+
* distributed under the License is distributed on an "AS IS" BASIS,
14+
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
15+
* See the License for the specific language governing permissions and
16+
* limitations under the License.
17+
*/
18+
19+
'use strict';
20+
21+
// MODULES //
22+
23+
var bench = require( '@stdlib/bench' );
24+
var randu = require( '@stdlib/random/base/randu' );
25+
var pkg = require( './../package.json' ).name;
26+
var incrnanmvmr = require( './../lib' );
27+
28+
29+
// MAIN //
30+
31+
bench( pkg, function benchmark( b ) {
32+
var f;
33+
var i;
34+
b.tic();
35+
for ( i = 0; i < b.iterations; i++ ) {
36+
f = incrnanmvmr( (i%5)+1 );
37+
if ( typeof f !== 'function' ) {
38+
b.fail( 'should return a function' );
39+
}
40+
}
41+
b.toc();
42+
if ( typeof f !== 'function' ) {
43+
b.fail( 'should return a function' );
44+
}
45+
b.pass( 'benchmark finished' );
46+
b.end();
47+
});
48+
49+
bench( pkg+'::accumulator', function benchmark( b ) {
50+
var acc;
51+
var v;
52+
var i;
53+
54+
acc = incrnanmvmr( 5 );
55+
56+
b.tic();
57+
for ( i = 0; i < b.iterations; i++ ) {
58+
v = acc( randu() );
59+
if ( v !== v ) {
60+
b.fail( 'should not return NaN' );
61+
}
62+
}
63+
b.toc();
64+
if ( v !== v ) {
65+
b.fail( 'should not return NaN' );
66+
}
67+
b.pass( 'benchmark finished' );
68+
b.end();
69+
});
70+
71+
bench( pkg+'::accumulator,known_mean', function benchmark( b ) {
72+
var acc;
73+
var v;
74+
var i;
75+
76+
acc = incrnanmvmr( 5, 0.5 );
77+
78+
b.tic();
79+
for ( i = 0; i < b.iterations; i++ ) {
80+
v = acc( randu() );
81+
if ( v !== v ) {
82+
b.fail( 'should not return NaN' );
83+
}
84+
}
85+
b.toc();
86+
if ( v !== v ) {
87+
b.fail( 'should not return NaN' );
88+
}
89+
b.pass( 'benchmark finished' );
90+
b.end();
91+
});

‎lib/node_modules/@stdlib/stats/incr/nanmvmr/docs/img/equation_arithmetic_mean.svg‎

Lines changed: 43 additions & 0 deletions
Loading

0 commit comments

Comments
 (0)