nanmeanwd

Calculate the arithmetic mean of a strided array, ignoring NaN values and using Welford's algorithm.

Usage

var nanmeanwd = require( '@stdlib/stats/base/nanmeanwd' );

nanmeanwd( N, x, stride )

Computes the arithmetic mean of a strided array x, ignoring NaN values and using Welford's algorithm.

var x = [ 1.0, -2.0, NaN, 2.0 ];
var N = x.length;

var v = nanmeanwd( N, x, 1 );
// returns ~0.3333

The function has the following parameters:

N: number of indexed elements.
x: input Array or typed array.
stride: index increment for x.

The N and stride parameters determine which elements in x are accessed at runtime. For example, to compute the arithmetic mean of every other element in x,

var floor = require( '@stdlib/math/base/special/floor' );

var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0, NaN ];
var N = floor( x.length / 2 );

var v = nanmeanwd( N, x, 2 );
// returns 1.25

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

var Float64Array = require( '@stdlib/array/float64' );
var floor = require( '@stdlib/math/base/special/floor' );

var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN ] );
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var N = floor( x0.length / 2 );

var v = nanmeanwd( N, x1, 2 );
// returns 1.25

nanmeanwd.ndarray( N, x, stride, offset )

Computes the arithmetic mean of a strided array, ignoring NaN values and using Welford's algorithm and alternative indexing semantics.

var x = [ 1.0, -2.0, NaN, 2.0 ];
var N = x.length;

var v = nanmeanwd.ndarray( N, x, 1, 0 );
// returns ~0.33333

The function has the following additional parameters:

offset: starting index for x.

While typed array views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to calculate the arithmetic mean for every other value in x starting from the second value

var floor = require( '@stdlib/math/base/special/floor' );

var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN ];
var N = floor( x.length / 2 );

var v = nanmeanwd.ndarray( N, x, 2, 1 );
// returns 1.25

Notes

If N <= 0, both functions return NaN.
If every indexed element is NaN, both functions return NaN.
Depending on the environment, the typed versions (dnanmeanwd, snanmeanwd, etc.) are likely to be significantly more performant.

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float64Array = require( '@stdlib/array/float64' );
var nanmeanwd = require( '@stdlib/stats/base/nanmeanwd' );

var x;
var i;

x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    if ( randu() < 0.2 ) {
        x[ i ] = NaN;
    } else {
        x[ i ] = round( (randu()*100.0) - 50.0 );
    }
}
console.log( x );

var v = nanmeanwd( x.length, x, 1 );
console.log( v );

References

Welford, B. P. 1962. "Note on a Method for Calculating Corrected Sums of Squares and Products." Technometrics 4 (3). Taylor & Francis: 419–20. doi:10.1080/00401706.1962.10490022.
van Reeken, A. J. 1968. "Letters to the Editor: Dealing with Neely's Algorithms." Communications of the ACM 11 (3): 149–50. doi:10.1145/362929.362961.