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dmeanstdev

Compute the arithmetic mean and standard deviation of a one-dimensional double-precision floating-point ndarray.

The population standard deviation of a finite size population of size N is given by

$$\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}$$

where the population mean is given by

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

Often in the analysis of data, the true population standard deviation is not known a priori and must be estimated from a sample drawn from the population distribution. If one attempts to use the formula for the population standard deviation, the result is biased and yields an uncorrected sample standard deviation. To compute a corrected sample standard deviation for a sample of size n,

$$s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}$$

where the sample mean is given by

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

The use of the term n-1 is commonly referred to as Bessel's correction. Note, however, that applying Bessel's correction can increase the mean squared error between the sample standard deviation and population standard deviation. Depending on the characteristics of the population distribution, other correction factors (e.g., n-1.5, n+1, etc) can yield better estimators.

Installation

npm install @stdlib/stats-base-ndarray-dmeanstdev

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 dmeanstdev = require( '@stdlib/stats-base-ndarray-dmeanstdev' );

dmeanstdev( arrays )

Computes the arithmetic mean and standard deviation of a one-dimensional double-precision floating-point ndarray.

var Float64Array = require( '@stdlib/array-float64' );
var scalar2ndarray = require( '@stdlib/ndarray-from-scalar' );
var ndarray = require( '@stdlib/ndarray-base-ctor' );

var opts = {
    'dtype': 'float64'
};

var xbuf = new Float64Array( [ 1.0, 3.0, 4.0, 2.0 ] );
var x = new ndarray( opts.dtype, xbuf, [ 4 ], [ 1 ], 0, 'row-major' );

var out = new ndarray( opts.dtype, new Float64Array( 2 ), [ 2 ], [ 1 ], 0, 'row-major' );

var correction = scalar2ndarray( 1.0, opts );

var v = dmeanstdev( [ x, out, correction ] );
// returns <ndarray>[ 2.5, ~1.2910 ]

The function has the following parameters:

• arrays: array-like object containing the following ndarrays in order:

  1. a one-dimensional input ndarray.
  2. a one-dimensional output ndarray to store the mean and standard deviation.
  3. a zero-dimensional ndarray specifying the degrees of freedom adjustment. Setting this to a value other than 0 has the effect of adjusting the divisor during the calculation of the standard deviation according to N-c where c corresponds to the provided degrees of freedom adjustment. When computing the standard deviation of a population, setting this to 0 is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the corrected sample standard deviation, setting this to 1 is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel's correction).

Notes

• If provided an empty one-dimensional ndarray, the computed arithmetic mean and standard deviation are equal to NaN.
• If N - c is less than or equal to 0 (where N corresponds to the number of elements in the input ndarray and c corresponds to the provided degrees of freedom adjustment), the computed arithmetic mean and standard deviation are equal to NaN.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var Float64Array = require( '@stdlib/array-float64' );
var scalar2ndarray = require( '@stdlib/ndarray-from-scalar' );
var ndarray = require( '@stdlib/ndarray-base-ctor' );
var ndarray2array = require( '@stdlib/ndarray-to-array' );
var dmeanstdev = require( '@stdlib/stats-base-ndarray-dmeanstdev' );

var opts = {
    'dtype': 'float64'
};

var xbuf = discreteUniform( 10, -50, 50, opts );
var x = new ndarray( opts.dtype, xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
console.log( ndarray2array( x ) );

var out = new ndarray( opts.dtype, new Float64Array( 2 ), [ 2 ], [ 1 ], 0, 'row-major' );

var correction = scalar2ndarray( 1.0, opts );

var v = dmeanstdev( [ x, out, correction ] );
console.log( ndarray2array( v ) );

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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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