time-to-botec

main.js (5672B)

---

 /**
 * @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 isCollection = require( '@stdlib/assert/is-collection' );
 var isPlainObject = require( '@stdlib/assert/is-plain-object' );
 var setReadOnly = require( '@stdlib/utils/define-read-only-property' );
 var objectKeys = require( '@stdlib/utils/keys' );
 var qnorm = require( './../../base/dists/normal/quantile' );
 var chisqCDF = require( './../../base/dists/chisquare/cdf' );
 var group = require( '@stdlib/utils/group' );
 var ranks = require( './../../ranks' );
 var abs = require( '@stdlib/math/base/special/abs' );
 var pow = require( '@stdlib/math/base/special/pow' );
 var indexOf = require( '@stdlib/utils/index-of' );
 var median = require( './median.js' );
 var validate = require( './validate.js' );
 var print = require( './print.js' ); // eslint-disable-line stdlib/no-redeclare
 
 
 // FUNCTIONS //
 
 /**
 * Returns an array of a chosen length filled with the supplied value.
 *
 * @private
 * @param {*} val - value to repeat
 * @param {NonNegativeInteger} len - array length
 * @returns {Array} filled array
 */
 function repeat( val, len ) {
 	var out = new Array( len );
 	var i;
 
 	for ( i = 0; i < len; i++ ) {
 		out[ i ] = val;
 	}
 	return out;
 }
 
 
 // MAIN //
 
 /**
 * Computes the Fligner-Killeen test for equal variances.
 *
 * @param {...NumericArray} arguments - either two or more number arrays or a single numeric array if an array of group indicators is supplied as an option
 * @param {Options} [options] - function options
 * @param {number} [options.alpha=0.05] - significance level
 * @param {Array} [options.groups] - array of group indicators
 * @throws {TypeError} must provide array-like arguments
 * @throws {RangeError} alpha option has to be a number in the interval `[0,1]`
 * @throws {Error} must provide at least two array-like arguments if `groups` is not set
 * @throws {TypeError} options has to be simple object
 * @throws {TypeError} must provide valid options
 * @returns {Object} test results
 *
 * @example
 * // Data from Hollander & Wolfe (1973), p. 116:
 * var x = [ 2.9, 3.0, 2.5, 2.6, 3.2 ];
 * var y = [ 3.8, 2.7, 4.0, 2.4 ];
 * var z = [ 2.8, 3.4, 3.7, 2.2, 2.0 ];
 *
 * var out = fligner( x, y, z );
 * // returns {...}
 */
 function fligner() {
 	var variance;
 	var options;
 	var ngroups;
 	var levels;
 	var groups;
 	var scores;
 	var table;
 	var alpha;
 	var delta;
 	var args;
 	var mean;
 	var opts;
 	var pval;
 	var sums;
 	var xabs;
 	var stat;
 	var err;
 	var loc;
 	var out;
 	var df;
 	var M2;
 	var a;
 	var n;
 	var x;
 	var i;
 	var j;
 
 	args = [];
 	ngroups = arguments.length;
 	opts = {};
 	if ( isPlainObject( arguments[ ngroups - 1 ] ) ) {
 		options = arguments[ ngroups - 1 ];
 		ngroups -= 1;
 		err = validate( opts, options );
 		if ( err ) {
 			throw err;
 		}
 	}
 	if ( opts.groups ) {
 		groups = opts.groups;
 		table = group( arguments[ 0 ], groups );
 		levels = objectKeys( table );
 		ngroups = levels.length;
 		if ( ngroups < 2 ) {
 			throw new Error( 'invalid number of groups. `groups` array must contain at least two unique elements. Value: `' + levels + '`.' );
 		}
 		for ( i = 0; i < ngroups; i++ ) {
 			args.push( table[ levels[ i ] ] );
 		}
 	} else {
 		groups = [];
 		for ( i = 0; i < ngroups; i++ ) {
 			args.push( arguments[ i ] );
 			groups = groups.concat( repeat( i, arguments[ i ].length ) );
 		}
 	}
 	if ( opts.alpha === void 0 ) {
 		alpha = 0.05;
 	} else {
 		alpha = opts.alpha;
 	}
 	if ( alpha < 0.0 || alpha > 1.0 ) {
 		throw new RangeError( 'invalid argument. Option `alpha` must be a number in the range 0 to 1. Value: `' + alpha + '`.' );
 	}
 	x = [];
 	for ( i = 0; i < ngroups; i++ ) {
 		if ( !isCollection( args[ i ] ) ) {
 			throw new TypeError( 'invalid argument. Must provide array-like arguments. Value: `' + args[ i ] + '`.' );
 		}
 		if ( args[ i ].length === 0 ) {
 			throw new Error( 'invalid argument. Supplied arrays cannot be empty. Value: `' + args[ i ] + '`.' );
 		}
 		loc = median( args[ i ] );
 		for ( j = 0; j < args[ i ].length; j++ ) {
 			args[ i ][ j ] -= loc;
 		}
 		x = x.concat( args[ i ] );
 	}
 	n = x.length;
 	xabs = new Array( n );
 	for ( i = 0; i < n; i++ ) {
 		xabs[ i ] = abs( x[ i ] );
 	}
 	scores = ranks( xabs );
 	a = new Array( n );
 	mean = 0.0;
 	M2 = 0.0;
 	sums = repeat( 0.0, ngroups );
 	for ( i = 0; i < n; i++ ) {
 		a[ i ] = qnorm( ( 1.0 + ( scores[ i ]/(n+1) ) ) / 2.0, 0.0, 1.0 );
 		sums[ ( levels ) ? indexOf( levels, groups[i] ) : groups[i] ] += a[ i ];
 		delta = a[ i ] - mean;
 		mean += delta / ( i+1 );
 		M2 += delta * ( a[ i ] - mean );
 	}
 	variance = M2 / ( n - 1 );
 	stat = 0.0;
 	for ( i = 0; i < ngroups; i++ ) {
 		stat += pow( sums[ i ], 2 ) / args[ i ].length;
 	}
 	stat = ( stat - ( n * pow( mean, 2 ) ) ) / variance;
 	df = ngroups - 1;
 	pval = 1.0 - chisqCDF( stat, df );
 
 	out = {};
 	setReadOnly( out, 'rejected', pval <= alpha );
 	setReadOnly( out, 'alpha', alpha );
 	setReadOnly( out, 'pValue', pval );
 	setReadOnly( out, 'statistic', stat );
 	setReadOnly( out, 'df', df );
 	setReadOnly( out, 'method', 'Fligner-Killeen test of homogeneity of variances' );
 	setReadOnly( out, 'print', print );
 	return out;
 }
 
 
 // EXPORTS //
 
 module.exports = fligner;