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incrmvmr
Compute a moving variance-to-mean ratio (VMR) incrementally.
For a window of size W
, the unbiased sample variance is defined as
and the arithmetic mean is defined as
The variance-to-mean ratio (VMR) is thus defined as
Usage
var incrmvmr = require( '@stdlib/stats/incr/mvmr' );
incrmvmr( window[, mean] )
Returns an accumulator function
which incrementally computes a moving variance-to-mean ratio. The window
parameter defines the number of values over which to compute the moving variance-to-mean ratio.
var accumulator = incrmvmr( 3 );
If the mean is already known, provide a mean
argument.
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.
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
Notes
-
Input values are not type checked. If provided
NaN
or a value which, when used in computations, results inNaN
, the accumulated value isNaN
for at leastW-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 firstW-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:
VMR Description Example Distribution 0 not dispersed constant 0 < VMR < 1 under-dispersed binomial 1 -- Poisson >1 over-dispersed geometric, negative-binomial Accordingly, one can use the 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 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 is also known as the index of dispersion, dispersion index, coefficient of dispersion, relative variance, and the Fano factor.
Examples
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() );