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* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MODULES //
var hasOwnProp = require( '@stdlib/assert/has-own-property' );
var isObject = require( '@stdlib/assert/is-plain-object' );
var isPositiveInteger = require( '@stdlib/assert/is-positive-integer' ).isPrimitive;
var isBoolean = require( '@stdlib/assert/is-boolean' ).isPrimitive;
var incrminmax = require( '@stdlib/stats/incr/minmax' );
var incrmeanstdev = require( '@stdlib/stats/incr/meanstdev' );
var setReadOnly = require( '@stdlib/utils/define-read-only-property' );
var setReadOnlyAccessor = require( '@stdlib/utils/define-read-only-accessor' );
var max = require( '@stdlib/math/base/special/max' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var roundn = require( '@stdlib/math/base/special/roundn' );
var tQuantile = require( '@stdlib/stats/base/dists/t/quantile' );
var format = require( '@stdlib/string/format' );
var validate = require( './validate.js' );
var defaults = require( './defaults.js' );
// MAIN //
/**
* Returns an accumulator function which incrementally performs Grubbs' test for detecting outliers.
*
* @param {Options} [options] - function options
* @param {number} [options.alpha=0.05] - significance level
* @param {string} [options.alternative='two-sided'] - alternative hypothesis ('two-sided', 'min', 'max')
* @param {NonNegativeInteger} [options.init=100] - number of data points used to compute initial statistics
* @throws {TypeError} options argument must be an object
* @throws {TypeError} must provide valid options
* @throws {RangeError} `alpha` option must be on the interval `[0,1]`
* @returns {Function} accumulator function
*
* @example
* var rnorm = require( '@stdlib/random/base/normal' );
*
* var accumulator;
* var opts;
* var res;
* var i;
*
* opts = {
* 'init': 100
* };
*
* accumulator = incrgrubbs( opts );
*
* for ( i = 0; i < 200; i++ ) {
* res = accumulator( rnorm( 10.0, 5.0 ) );
* }
*/
function incrgrubbs() {
var meanstdev;
var results;
var minmax;
var opts;
var err;
var mm;
var ms;
var gc;
var df;
var N;
var G;
opts = defaults();
if ( arguments.length ) {
err = validate( opts, arguments[ 0 ] );
if ( err ) {
throw err;
}
}
// Initialize the results object:
results = {};
setReadOnlyAccessor( results, 'rejected', getRejected );
setReadOnly( results, 'alpha', opts.alpha );
setReadOnlyAccessor( results, 'criticalValue', getCriticalValue );
setReadOnlyAccessor( results, 'statistic', getStatistic );
setReadOnlyAccessor( results, 'df', getDOF );
setReadOnlyAccessor( results, 'mean', getMean );
setReadOnlyAccessor( results, 'sd', getStDev );
setReadOnlyAccessor( results, 'min', getMin );
setReadOnlyAccessor( results, 'max', getMax );
setReadOnly( results, 'alt', opts.alternative );
setReadOnly( results, 'method', 'Grubbs\' Test' );
setReadOnly( results, 'print', print );
N = 0;
df = 0;
G = 0.0;
gc = 0.0;
// Initialize statistics accumulators:
mm = [ 0.0, 0.0 ];
minmax = incrminmax( mm );
ms = [ 0.0, 0.0 ];
meanstdev = incrmeanstdev( ms );
return accumulator;
/**
* If provided a value, the accumulator function returns updated Grubbs' test results. If not provided a value, the accumulator function returns the current Grubbs' test results.
*
* @private
* @param {number} [x] - new value
* @returns {(Object|null)} test results or null
*/
function accumulator( x ) {
var sig;
var md;
var tc;
if ( arguments.length === 0 ) {
if ( N < opts.init || df <= 0 ) {
return null;
}
return results;
}
N += 1;
// Update model statistics:
meanstdev( x );
minmax( x );
// Compute the degrees of freedom:
df = N - 2;
if ( N < opts.init || df <= 0 ) {
return null;
}
// Compute the test statistic and significance level...
if ( opts.alternative === 'min' ) {
G = ( ms[0]-mm[0] ) / ms[ 1 ];
sig = opts.alpha / N;
} else if ( opts.alternative === 'max' ) {
G = ( mm[1]-ms[0] ) / ms[ 1 ];
sig = opts.alpha / N;
} else { // two-sided
md = max( ms[0]-mm[0], mm[1]-ms[0] ); // maximum absolute deviation
G = md / ms[ 1 ];
sig = opts.alpha / (2*N);
}
// Compute the critical values:
tc = tQuantile( 1.0-sig, df );
gc = (N-1)*tc / sqrt( N*(df+(tc*tc)) );
return results;
}
/**
* Returns a `boolean` indicating whether the null hypothesis should be rejected.
*
* @private
* @returns {boolean} boolean indicating whether the null hypothesis should be rejected
*/
function getRejected() {
return ( G > gc );
}
/**
* Returns the critical value.
*
* @private
* @returns {number} critical value
*/
function getCriticalValue() {
return gc;
}
/**
* Returns the test statistic.
*
* @private
* @returns {number} test statistic
*/
function getStatistic() {
return G;
}
/**
* Returns the degrees of freedom (DOF).
*
* @private
* @returns {PositiveInteger} degrees of freedom
*/
function getDOF() {
return df;
}
/**
* Returns the sample mean.
*
* @private
* @returns {number} sample mean
*/
function getMean() {
return ms[ 0 ];
}
/**
* Returns the corrected sample standard deviation.
*
* @private
* @returns {number} corrected sample standard deviation
*/
function getStDev() {
return ms[ 1 ];
}
/**
* Returns the sample minimum.
*
* @private
* @returns {number} sample minimum
*/
function getMin() {
return mm[ 0 ];
}
/**
* Returns the sample maximum.
*
* @private
* @returns {number} sample maximum
*/
function getMax() {
return mm[ 1 ];
}
/**
* Pretty-print test results.
*
* @private
* @param {Object} [options] - options object
* @param {PositiveInteger} [options.digits=4] - number of digits after the decimal point
* @param {boolean} [options.decision=true] - boolean indicating whether to print the test decision
* @throws {TypeError} options argument must be an object
* @throws {TypeError} must provide valid options
* @returns {string} formatted output
*/
function print( options ) {
var decision;
var digits;
var str;
digits = opts.digits;
decision = opts.decision;
if ( arguments.length > 0 ) {
if ( !isObject( options ) ) {
throw new TypeError( format( 'invalid argument. Must provide an object. Value: `%s`.', options ) );
}
if ( hasOwnProp( options, 'digits' ) ) {
if ( !isPositiveInteger( options.digits ) ) {
throw new TypeError( format( 'invalid option. `%s` option must be a positive integer. Option: `%s`.', 'digits', options.digits ) );
}
digits = options.digits;
}
if ( hasOwnProp( options, 'decision' ) ) {
if ( !isBoolean( options.decision ) ) {
throw new TypeError( format( 'invalid option. `%s` option must be a boolean. Option: `%s`.', 'decision', options.decision ) );
}
decision = options.decision;
}
}
str = '';
str += results.method;
str += '\n\n';
str += 'Alternative hypothesis: ';
if ( opts.alternative === 'max' ) {
str += 'The maximum value (' + mm[ 1 ] + ') is an outlier';
} else if ( opts.alternative === 'min' ) {
str += 'The minimum value (' + mm[ 0 ] + ') is an outlier';
} else { // two-sided
str += 'The ';
if ( ms[0]-mm[0] > mm[1]-ms[0] ) {
str += 'minimum value (' + mm[ 0 ] + ')';
} else {
str += 'maximum value (' + mm[ 1 ] + ')';
}
str += ' is an outlier';
}
str += '\n\n';
str += ' criticalValue: ' + roundn( gc, -digits ) + '\n';
str += ' statistic: ' + roundn( G, -digits ) + '\n';
str += ' df: ' + df + '\n';
str += '\n';
if ( decision ) {
str += 'Test Decision: ';
if ( G > gc ) {
str += 'Reject null in favor of alternative at ' + (opts.alpha*100.0) + '% significance level';
} else {
str += 'Fail to reject null in favor of alternative at ' + (opts.alpha*100.0) + '% significance level';
}
str += '\n';
}
return str;
}
}
// EXPORTS //
module.exports = incrgrubbs;
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