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dmeanlipw

Calculate the arithmetic mean of a double-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation.

The arithmetic mean is defined as

$$\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i$$

Installation

npm install @stdlib/stats-base-dmeanlipw

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

dmeanlipw( N, x, stride )

Computes the arithmetic mean of a double-precision floating-point strided array x using a one-pass trial mean algorithm with pairwise summation.

var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

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

The function has the following parameters:

• N: number of indexed elements.
• x: input Float64Array.
• 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 Float64Array = require( '@stdlib/array-float64' );
var floor = require( '@stdlib/math-base-special-floor' );

var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
var N = floor( x.length / 2 );

var v = dmeanlipw( 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 ] );
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

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

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

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

Computes the arithmetic mean of a double-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation and alternative indexing semantics.

var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

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

var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var N = floor( x.length / 2 );

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

Notes

• If N <= 0, both functions return NaN.
• The underlying algorithm is a specialized case of Welford's algorithm. Similar to the method of assumed mean, the first strided array element is used as a trial mean. The trial mean is subtracted from subsequent data values, and the average deviations used to adjust the initial guess. Accordingly, the algorithm's accuracy is best when data is unordered (i.e., the data is not sorted in either ascending or descending order such that the first value is an "extreme" value).

Examples

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

var x;
var i;

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

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

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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.
• Ling, Robert F. 1974. "Comparison of Several Algorithms for Computing Sample Means and Variances." Journal of the American Statistical Association 69 (348). American Statistical Association, Taylor & Francis, Ltd.: 859–66. doi:10.2307/2286154.
• Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." SIAM Journal on Scientific Computing 14 (4): 783–99. doi:10.1137/0914050.

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See Also

• @stdlib/stats-base/dmean: calculate the arithmetic mean of a double-precision floating-point strided array.
• @stdlib/stats-base/dmeanli: calculate the arithmetic mean of a double-precision floating-point strided array using a one-pass trial mean algorithm.
• @stdlib/stats-base/dmeanpw: calculate the arithmetic mean of a double-precision floating-point strided array using pairwise summation.
• @stdlib/stats-base/smeanlipw: calculate the arithmetic mean of a single-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation.

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Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

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License

See LICENSE.

Copyright

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