Midsummary

Computes a trimmed midrange (midsummary) of a numeric array.

The midsummary, or n% trimmed midrange, is the average of the n% and (100-n)% percentiles, and has a breakdown point of n%. The midsummary is a descriptive statistic and also an L-estimator of central location or skewness. Notably, differences between midsummaries, such as between the midhinge and the median, describe skewness at different points in a distribution's tail.

Special Cases:

• The 50% midsummary equates to the median (see compute-median).
• The 25% midsummary is the midhinge (see compute-midhinge).
• The 0% midsummary is the midrange ( see compute-midrange).

Installation

$ npm install compute-midsummary

For use in the browser, use browserify.

Usage

To use the module,

var midsummary = require( 'compute-midsummary' );

midsummary( arr, n[, opts] )

Computes the n% midsummary of a numeric array. n exists on the interval [0.0, 0.50] and specifies the proportion of values to discard in the distribution tails.

var unsorted = [ 8, 2, 3, 9, 5, 1, 4, 10, 7, 0, 6 ];

var mids = midsummary( unsorted, 0.25 );
// returns 5

If the input array is already sorted in ascending order, set the sorted options flag to true.

var sorted = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ];

var mids = midsummary( sorted, 0.25, {'sorted': true} );
// returns 5

Additional options are the same as for the quantile module.

Examples

var data = new Array( 100 );

for ( var i = 0; i < data.length; i++ ) {
    data[ i ] = Math.round( Math.random()*100 );
}

console.log( midsummary( data, 0.10 ) );

To run the example code from the top-level application directory,

$ node ./examples/index.js

Tests

Unit

Unit tests use the Mocha test framework with Chai assertions. To run the tests, execute the following command in the top-level application directory:

$ make test

All new feature development should have corresponding unit tests to validate correct functionality.

Test Coverage

This repository uses Istanbul as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:

$ make test-cov

Istanbul creates a ./reports/coverage directory. To access an HTML version of the report,

$ make view-cov

License

MIT license.

Copyright

Copyright © 2014. Rebekah Smith.