dmeanstdev

Calculate the mean and standard deviation of a double-precision floating-point strided array.

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

where the population mean is given by

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,

where the sample mean is given by

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-strided-dmeanstdev

Usage

var dmeanstdev = require( '@stdlib/stats-strided-dmeanstdev' );

dmeanstdev( N, correction, x, strideX, out, strideOut )

Computes the mean and standard deviation of a double-precision floating-point strided array.

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

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var out = new Float64Array( 2 );

var v = dmeanstdev( x.length, 1, x, 1, out, 1 );
// returns <Float64Array>[ ~0.3333, ~2.0817 ]

var bool = ( v === out );
// returns true

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 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 parameter 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 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.
• strideX: stride length for x.
• out: output Float64Array for storing results.
• strideOut: stride length for out.

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

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 ] );
var out = new Float64Array( 2 );

var v = dmeanstdev( 4, 1, x, 2, out, 1 );
// returns <Float64Array>[ 1.25, 2.5 ]

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

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

var out0 = new Float64Array( 4 );
var out1 = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

var v = dmeanstdev( 4, 1, x1, 2, out1, 1 );
// returns <Float64Array>[ 1.25, 2.5 ]

dmeanstdev.ndarray( N, correction, x, strideX, offsetX, out, strideOut, offsetOut )

Computes the mean and standard deviation of a double-precision floating-point strided array and alternative indexing semantics.

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

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var out = new Float64Array( 2 );

var v = dmeanstdev.ndarray( x.length, 1, x, 1, 0, out, 1, 0 );
// returns <Float64Array>[ ~0.3333, ~2.0817 ]

The function has the following additional parameters:

• offsetX: starting index for x.
• offsetOut: starting index for out.

While typed array views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example, to calculate the mean and standard deviation for every other element in x starting from the second element

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 ] );
var out = new Float64Array( 4 );

var v = dmeanstdev.ndarray( 4, 1, x, 2, 1, out, 2, 1 );
// returns <Float64Array>[ 0.0, 1.25, 0.0, 2.5 ]

Notes

• If N <= 0, both functions return a mean and standard deviation equal to NaN.
• If N - c is less than or equal to 0 (where c corresponds to the provided degrees of freedom adjustment), both functions return a standard deviation equal to NaN.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var Float64Array = require( '@stdlib/array-float64' );
var dmeanstdev = require( '@stdlib/stats-strided-dmeanstdev' );

var x = discreteUniform( 10, -50, 50, {
    'dtype': 'float64'
});
console.log( x );

var out = new Float64Array( 2 );
dmeanstdev( x.length, 1, x, 1, out, 1 );
console.log( out );

C APIs

Usage

#include "stdlib/stats/strided/dmeanstdev.h"

stdlib_strided_dmeanstdev( N, correction, *X, strideX, *Out, strideOut )

Computes the mean and standard deviation of a double-precision floating-point strided array.

const double x[] = { 1.0, -2.0, 2.0 };
double out[] = { 0.0, 0.0 };

stdlib_strided_dmeanstdev( 4, 1.0, x, 1, out, 1 );

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 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 parameter 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 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.
• Out: [out] double* output array.
• strideOut: [in] CBLAS_INT stride length for Out.

void stdlib_strided_dmeanstdev( const CBLAS_INT N, const double correction, const double *X, const CBLAS_INT strideX, double *Out, const CBLAS_INT strideOut );

stdlib_strided_dmeanstdev_ndarray( N, correction, *X, strideX, offsetX, *Out, strideOut, offsetOut )

Computes the mean and standard deviation of a double-precision floating-point strided array using alternative indexing semantics.

const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
double out[] = { 0.0, 0.0 };

stdlib_strided_dmeanstdev_ndarray( 4, 1.0, x, 2, 0, x, 1, 0 );

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 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 parameter 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 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.
• Out: [out] double* output array.
• strideOut: [in] CBLAS_INT stride length for Out.
• offsetOut: [in] CBLAS_INT starting index for Out.

void stdlib_strided_dmeanstdev_ndarray( const CBLAS_INT N, const double correction, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, double *Out, const CBLAS_INT strideOut, const CBLAS_INT offsetOut );

Examples

#include "stdlib/stats/strided/dmeanstdev.h"
#include <stdio.h>

int main( void ) {
    // Create a strided array:
    const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };

    // Create an output array:
    double out[] = { 0.0, 0.0 };

    // Specify the number of elements:
    const int N = 4;

    // Specify the stride length:
    const int strideX = 2;
    const int strideOut = 1;

    // Compute the mean and standard deviation:
    stdlib_strided_dmeanstdev( N, 1.0, x, strideX, out, strideOut );

    // Print the result:
    printf( "sample mean: %lf\n", out[ 0 ] );
    printf( "sample standard deviation: %lf\n", out[ 1 ] );
}

See Also

• @stdlib/stats-strided/dmean: calculate the arithmetic mean of a double-precision floating-point strided array.
• @stdlib/stats-strided/dmeanvar: calculate the mean and variance of a double-precision floating-point strided array.
• @stdlib/stats-strided/dstdev: calculate the standard deviation of a double-precision floating-point strided array.

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.

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License

See LICENSE.

Copyright

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