// wink-statistics
// Fast and Numerically Stable Statistical Analysis Utilities.
//
// Copyright (C) GRAYPE Systems Private Limited
//
// This file is part of “wink-statistics”.
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
// ## streaming
var getValidFD = require( './get-valid-fd.js' );
// ### stdev
/**
*
* Standard Deviation is computed incrementally with arrival of each value from the data stream.
*
* The [`compute()`](https://winkjs.org/wink-statistics/Stream.html#compute) requires
* a single numeric value as argument.
* The computations are inspired by the method proposed by [B. P. Welford](http://dx.doi.org/10.1080/00401706.1962.10490022).
*
* The [`result()`](https://winkjs.org/wink-statistics/Stream.html#result) returns
* returns an object containing sample `stdev` and
* `variance`, along with `mean`, `size` of data; it also
* contains population standard deviation and variance as `stdevp` and `variancep`.
*
* @memberof streaming#
* @return {Stream} Object containing methods such as `compute()`, `result()` & `reset()`.
* @example
* var sd = stdev();
* sd.compute( 2 );
* sd.compute( 3 );
* sd.compute( 5 );
* sd.compute( 7 );
* sd.value();
* // returns 2.2174
* sd.result();
* // returns { size: 4, mean: 4.25,
* // variance: 4.9167,
* // stdev: 2.2174,
* // variancep: 3.6875,
* // stdevp: 1.9203
* // }
*/
var stdev = function () {
var mean = 0;
var varianceXn = 0;
var items = 0;
var methods = Object.create( null );
methods.compute = function ( di ) {
var prevMean;
items += 1;
prevMean = mean;
mean += ( di - mean ) / items;
varianceXn += ( di - prevMean ) * ( di - mean );
return undefined;
}; // compute()
// This returns the sample standard deviation.
methods.value = function ( fractionDigits ) {
var fd = getValidFD( fractionDigits );
return ( items > 1 ) ? +( Math.sqrt( varianceXn / ( items - 1 ) ) ).toFixed( fd ) : 0;
}; // value()
// This returns the sample standard deviation along with host of other statistics.
methods.result = function ( fractionDigits ) {
var fd = getValidFD( fractionDigits );
var obj = Object.create( null );
var variance = ( items > 1 ) ? ( varianceXn / ( items - 1 ) ) : 0;
var variancep = ( items ) ? ( varianceXn / items ) : 0;
obj.size = items;
obj.mean = +mean.toFixed( fd );
// Sample variance & standard deviation.
obj.variance = +variance.toFixed( fd );
obj.stdev = +( Math.sqrt( variance ) ).toFixed( fd );
// Population variance & standard deviation.
obj.variancep = +variancep.toFixed( fd );
obj.stdevp = +( Math.sqrt( variancep ) ).toFixed( fd );
return obj;
}; // result()
methods.reset = function () {
mean = 0;
varianceXn = 0;
items = 0;
}; // reset()
return methods;
}; // stdev()
module.exports = stdev;