@stdlib/stats-base-dnanvariancepn

Calculate the variance of a double-precision floating-point strided array ignoring NaN values and using a two-pass algorithm.

https://github.com/stdlib-js/stats-base-dnanvariancepn

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array deviation dispersion javascript math mathematics node node-js nodejs sample-variance standard-deviation statistics stats stdlib strided strided-array typed unbiased var variance

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Calculate the variance of a double-precision floating-point strided array ignoring NaN values and using a two-pass algorithm.

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License: apache-2.0
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array deviation dispersion javascript math mathematics node node-js nodejs sample-variance standard-deviation statistics stats stdlib strided strided-array typed unbiased var variance

Created over 4 years ago · Last pushed 9 months ago

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We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

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dnanvariancepn

Calculate the variance of a double-precision floating-point strided array ignoring NaN values and using a two-pass algorithm.

The population [variance][variance] of a finite size population of size `N` is given by ```math \sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 ``` where the population mean is given by ```math \mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i ``` Often in the analysis of data, the true population [variance][variance] 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 [variance][variance], the result is biased and yields a **biased sample variance**. To compute an **unbiased sample variance** for a sample of size `n`, ```math s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 ``` where the sample mean is given by ```math \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 variance and population variance. Depending on the characteristics of the population distribution, other correction factors (e.g., `n-1.5`, `n+1`, etc) can yield better estimators.

## Installation ```bash npm install @stdlib/stats-base-dnanvariancepn ``` Alternatively, - To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]). - If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions). - For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]). The [branches.md][branches-url] 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 ```javascript var dnanvariancepn = require( '@stdlib/stats-base-dnanvariancepn' ); ``` #### dnanvariancepn( N, correction, x, strideX ) Computes the [variance][variance] of a double-precision floating-point strided array ignoring `NaN` values and using a two-pass algorithm. ```javascript var Float64Array = require( '@stdlib/array-float64' ); var x = new Float64Array( [ 1.0, -2.0, NaN, 2.0 ] ); var v = dnanvariancepn( x.length, 1, x, 1 ); // returns ~4.3333 ``` The function has the following parameters: - **N**: number of indexed elements. - **correction**: degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [variance][variance] according to `n-c` where `c` corresponds to the provided degrees of freedom adjustment and `n` corresponds to the number of non-`NaN` indexed elements. When computing the [variance][variance] of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the unbiased sample [variance][variance], setting this parameter 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). - **x**: input [`Float64Array`][@stdlib/array/float64]. - **strideX**: stride length for `x`. The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute the [variance][variance] of every other element in `x`, ```javascript var Float64Array = require( '@stdlib/array-float64' ); var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0, NaN, NaN ] ); // eslint-disable-line max-len var v = dnanvariancepn( 5, 1, x, 2 ); // returns 6.25 ``` Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. ```javascript var Float64Array = require( '@stdlib/array-float64' ); var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN, NaN ] ); // eslint-disable-line max-len var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element var v = dnanvariancepn( 5, 1, x1, 2 ); // returns 6.25 ``` #### dnanvariancepn.ndarray( N, correction, x, strideX, offsetX ) Computes the [variance][variance] of a double-precision floating-point strided array ignoring `NaN` values and using a two-pass algorithm and alternative indexing semantics. ```javascript var Float64Array = require( '@stdlib/array-float64' ); var x = new Float64Array( [ 1.0, -2.0, NaN, 2.0 ] ); var v = dnanvariancepn.ndarray( x.length, 1, x, 1, 0 ); // returns ~4.33333 ``` The function has the following additional parameters: - **offsetX**: starting index for `x`. While [`typed array`][mdn-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 [variance][variance] for every other element in `x` starting from the second element ```javascript var Float64Array = require( '@stdlib/array-float64' ); var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN, NaN ] ); // eslint-disable-line max-len var v = dnanvariancepn.ndarray( 5, 1, x, 2, 1 ); // returns 6.25 ```

## Notes - If `N <= 0`, both functions return `NaN`. - If `n - c` is less than or equal to `0` (where `c` corresponds to the provided degrees of freedom adjustment and `n` corresponds to the number of non-`NaN` indexed elements), both functions return `NaN`.

## Examples ```javascript var uniform = require( '@stdlib/random-base-uniform' ); var filledarrayBy = require( '@stdlib/array-filled-by' ); var bernoulli = require( '@stdlib/random-base-bernoulli' ); var dnanvariancepn = require( '@stdlib/stats-base-dnanvariancepn' ); function rand() { if ( bernoulli( 0.8 ) < 1 ) { return NaN; } return uniform( -50.0, 50.0 ); } var x = filledarrayBy( 10, 'float64', rand ); console.log( x ); var v = dnanvariancepn( x.length, 1, x, 1 ); console.log( v ); ```

## C APIs

### Usage ```c #include "stdlib/stats/base/dnanvariancepn.h" ``` #### stdlib_strided_dnanvariancepn( N, correction, \*X, strideX ) Computes the [variance][variance] of a double-precision floating-point strided array ignoring `NaN` values and using a two-pass algorithm. ```c const double x[] = { 1.0, -2.0, 0.0/0.0, 2.0 }; double v = stdlib_strided_dnanvariancepn( 4, 1.0, x, 1 ); // returns ~4.3333 ``` The function accepts the following arguments: - **N**: `[in] CBLAS_INT` number of indexed elements. - **correction**: `[in] double` degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [variance][variance] according to `n-c` where `c` corresponds to the provided degrees of freedom adjustment and `n` corresponds to the number of non-`NaN` indexed elements. When computing the [variance][variance] of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the unbiased sample [variance][variance], setting this parameter 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). - **X**: `[in] double*` input array. - **strideX**: `[in] CBLAS_INT` stride length for `X`. ```c double stdlib_strided_dnanvariancepn( const CBLAS_INT N, const double correction, const double *X, const CBLAS_INT strideX ); ``` #### stdlib_strided_dnanvariancepn_ndarray( N, correction, \*X, strideX, offsetX ) Computes the [variance][variance] of a double-precision floating-point strided array ignoring `NaN` values and using a two-pass algorithm and alternative indexing semantics. ```c const double x[] = { 1.0, -2.0, 0.0/0.0, 2.0 }; double v = stdlib_strided_dnanvariancepn_ndarray( 4, 1.0, x, 1, 0 ); // returns ~4.3333 ``` The function accepts the following arguments: - **N**: `[in] CBLAS_INT` number of indexed elements. - **correction**: `[in] double` degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [variance][variance] according to `n-c` where `c` corresponds to the provided degrees of freedom adjustment and `n` corresponds to the number of non-`NaN` indexed elements. When computing the [variance][variance] of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the unbiased sample [variance][variance], setting this parameter 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). - **X**: `[in] double*` input array. - **strideX**: `[in] CBLAS_INT` stride length for `X`. - **offsetX**: `[in] CBLAS_INT` starting index for `X`. ```c double stdlib_strided_dnanvariancepn_ndarray( const CBLAS_INT N, const double correction, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX ); ```

### Examples ```c #include "stdlib/stats/base/dnanvariancepn.h" #include int main( void ) { // Create a strided array: const double x[] = { 1.0, 2.0, 0.0/0.0, 3.0, 0.0/0.0, 4.0, 5.0, 6.0, 0.0/0.0, 7.0, 8.0, 0.0/0.0 }; // Specify the number of elements: const int N = 6; // Specify the stride length: const int strideX = 2; // Compute the variance: double v = stdlib_strided_dnanvariancepn( N, 1.0, x, strideX ); // Print the result: printf( "sample variance: %lf\n", v ); } ```

## References - Neely, Peter M. 1966. "Comparison of Several Algorithms for Computation of Means, Standard Deviations and Correlation Coefficients." _Communications of the ACM_ 9 (7). Association for Computing Machinery: 496–99. doi:[10.1145/365719.365958][@neely:1966a]. - Schubert, Erich, and Michael Gertz. 2018. "Numerically Stable Parallel Computation of (Co-)Variance." In _Proceedings of the 30th International Conference on Scientific and Statistical Database Management_. New York, NY, USA: Association for Computing Machinery. doi:[10.1145/3221269.3223036][@schubert:2018a].

* * * ## Notice This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib]. #### Community [![Chat][chat-image]][chat-url] --- ## License See [LICENSE][stdlib-license]. ## Copyright Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].

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npmjs.org: @stdlib/stats-base-dnanvariancepn

Calculate the variance of a double-precision floating-point strided array ignoring NaN values and using a two-pass algorithm.

Homepage: https://stdlib.io
License: Apache-2.0
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published over 1 year ago

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@stdlib/stats-base-dnanvariancepn

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