incrmhmean

Compute a moving harmonic mean incrementally.

The harmonic mean of positive real numbers x_0, x_1, ..., x_{n-1} is defined as

StartLayout 1st Row 1st Column upper H 2nd Column equals StartStartFraction n OverOver StartFraction 1 Over x 0 EndFraction plus StartFraction 1 Over x 1 EndFraction plus midline-horizontal-ellipsis plus StartFraction 1 Over x Subscript n minus 1 Baseline EndFraction EndEndFraction 2nd Row 1st Column Blank 2nd Column equals StartStartFraction n OverOver sigma-summation Underscript i equals 0 Overscript n minus 1 Endscripts StartFraction 1 Over x Subscript i Baseline EndFraction EndEndFraction 3rd Row 1st Column Blank 2nd Column equals left-parenthesis StartStartFraction sigma-summation Underscript i equals 0 Overscript n minus 1 Endscripts StartFraction 1 Over x Subscript i Baseline EndFraction OverOver n EndEndFraction right-parenthesis Superscript negative 1 EndLayout

Usage

var incrmhmean = require( '@stdlib/stats/incr/mhmean' );

incrmhmean( window )

Returns an accumulator function which incrementally computes a moving harmonic mean. The window parameter defines the number of values over which to compute the moving harmonic mean.

var accumulator = incrmhmean( 3 );

accumulator( [x] )

If provided an input value x, the accumulator function returns an updated harmonic mean. If not provided an input value x, the accumulator function returns the current harmonic-mean.

var accumulator = incrmhmean( 3 );

var v = accumulator();
// returns null

// Fill the window...
v = accumulator( 2.0 ); // [2.0]
// returns 2.0

v = accumulator( 1.0 ); // [2.0, 1.0]
// returns ~1.33

v = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
// returns ~1.64

// Window begins sliding...
v = accumulator( 7.0 ); // [1.0, 3.0, 7.0]
// returns ~2.03

v = accumulator( 5.0 ); // [3.0, 7.0, 5.0]
// returns ~4.44

v = accumulator();
// returns ~4.44

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.

Examples

var randu = require( '@stdlib/random/base/randu' );
var incrmhmean = require( '@stdlib/stats/incr/mhmean' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = incrmhmean( 5 );

// For each simulated datum, update the moving harmonic mean...
for ( i = 0; i < 100; i++ ) {
    v = randu() * 100.0;
    accumulator( v );
}
console.log( accumulator() );