Skip to content

nanstdevtk

Directory actions

More options

Directory actions

More options

Latest commit

 

History

History

nanstdevtk

Folders and files

NameName
Last commit message
Last commit date

parent directory

..
benchmark
benchmark
 
 
docs
docs
 
 
examples
examples
 
 
lib
lib
 
 
test
test
 
 
README.md
README.md
 
 
package.json
package.json
 
 

README.md

nanstdevtk

Calculate the standard deviation of an array ignoring NaN values and using a one-pass textbook algorithm.

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.

Usage

var nanstdevtk = require( '@stdlib/stats/array/nanstdevtk' );

nanstdevtk( x[, correction] )

Computes the standard deviation of an array ignoring NaN values and using a one-pass textbook algorithm.

var x = [ 1.0, -2.0, NaN, 2.0 ];

var v = nanstdevtk( x );
// returns ~2.0817

The function has the following parameters:

  • x: input array.
  • 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 N corresponds to the number of non-NaN array elements and 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 unbiased 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). Default: 1.0.

By default, the function computes the sample standard deviation. To adjust the degrees of freedom when computing the standard deviation, provide a correction argument.

var x = [ 1.0, -2.0, NaN, 2.0 ];

var v = nanstdevtk( x, 0.0 );
// returns ~1.6997

Notes

  • If provided an empty array, the function returns 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 array elements), the function returns NaN.
  • The function supports array-like objects having getter and setter accessors for array element access (e.g., @stdlib/array/base/accessor).
  • Some caution should be exercised when using the one-pass textbook algorithm. Literature overwhelmingly discourages the algorithm's use for two reasons: 1) the lack of safeguards against underflow and overflow and 2) the risk of catastrophic cancellation when subtracting the two sums if the sums are large and the variance small. These concerns have merit; however, the one-pass textbook algorithm should not be dismissed outright. For data distributions with a moderately large standard deviation to mean ratio (i.e., coefficient of variation), the one-pass textbook algorithm may be acceptable, especially when performance is paramount and some precision loss is acceptable (including a risk of computing a negative variance due to floating-point rounding errors!). In short, no single "best" algorithm for computing the standard deviation exists. The "best" algorithm depends on the underlying data distribution, your performance requirements, and your minimum precision requirements. When evaluating which algorithm to use, consider the relative pros and cons, and choose the algorithm which best serves your needs.

Examples

var uniform = require( '@stdlib/random/base/uniform' );
var filledarrayBy = require( '@stdlib/array/filled-by' );
var bernoulli = require( '@stdlib/random/base/bernoulli' );
var nanstdevtk = require( '@stdlib/stats/array/nanstdevtk' );

function rand() {
    if ( bernoulli( 0.8 ) < 1 ) {
        return NaN;
    }
    return uniform( -50.0, 50.0 );
}

var x = filledarrayBy( 10, 'generic', rand );
console.log( x );

var v = nanstdevtk( x );
console.log( v );