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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 isTypedArrayLike = require( '@stdlib/assert/is-typed-array-like' );
var isNumber = require( '@stdlib/assert/is-number' );
var isNumberArray = require( '@stdlib/assert/is-number-array' ).primitives;
var setReadOnly = require( '@stdlib/utils/define-read-only-property' );
var isFunction = require( '@stdlib/assert/is-function' );
var isString = require( '@stdlib/assert/is-string' ).isPrimitive;
var format = require( '@stdlib/string/format' );
var isnan = require( '@stdlib/assert/is-nan' );
var max = require( '@stdlib/stats/strided/max' );
var pKolmogorov1 = require( './smirnov.js' );
var pKolmogorov = require( './marsaglia.js' );
var ascending = require( './ascending.js' );
var subtract = require( './subtract.js' );
var validate = require( './validate.js' );
var getCDF = require( './get_cdf.js' );
var print = require( './print.js' ); // eslint-disable-line stdlib/no-redeclare
// FUNCTIONS //
var slice = Array.prototype.slice;
// MAIN //
/**
* Computes a Kolmogorov-Smirnov goodness-of-fit test.
*
* @param {NumericArray} x - input array holding numeric values
* @param {(Function|string)} y - either a CDF function or a string denoting the name of a distribution
* @param {...number} [params] - distribution parameters passed to reference CDF
* @param {Options} [options] - function options
* @param {number} [options.alpha=0.05] - significance level
* @param {boolean} [options.sorted=false] - boolean indicating if the input array is already in sorted order
* @param {string} [options.alternative="two-sided"] - string indicating whether to conduct two-sided or one-sided hypothesis test (other options: `less`, `greater`)
* @throws {TypeError} argument x has to be a typed array or array of numbers
* @throws {TypeError} argument y has to be a CDF function or string
* @throws {TypeError} options must be an object
* @throws {TypeError} alpha option has to be a number
* @throws {RangeError} alpha option has to be a number in the interval `[0,1]`
* @throws {TypeError} alternative option has to be a string
* @throws {Error} alternative option must be `two-sided`, `less` or `greater`
* @throws {TypeError} sorted option has to be a boolean
* @returns {Object} test result object
*
* @example
* var out = kstest( [ 2.0, 1.0, 5.0, -5.0, 3.0, 0.5, 6.0 ], 'normal', 0.0, 1.0 );
* // returns { 'pValue': ~0.015, 'statistic': ~0.556, ... }
*/
function kstest() {
var nDistParams;
var distParams;
var distArgs;
var options;
var alpha;
var opts;
var pval;
var stat;
var yVal;
var alt;
var err;
var idx;
var out;
var val;
var i;
var n;
var x;
var y;
x = arguments[ 0 ];
y = arguments[ 1 ];
if ( !isNumberArray( x ) && !isTypedArrayLike( x ) ) {
throw new TypeError( format( 'invalid argument. First argument must be a typed array or number array. Value: `%s`.', x ) );
}
if ( !isFunction( y ) && !isString( y ) ) {
throw new TypeError( format( 'invalid argument. Second argument must be either a CDF function or a string. Value: `%s`.', y ) );
}
if ( isString( y ) ) {
y = getCDF( y );
}
nDistParams = y.length - 1.0;
n = x.length;
distParams = new Array( nDistParams ); // eslint-disable-line stdlib/no-new-array
for ( i = 0; i < nDistParams; i++ ) {
idx = i + 2;
val = arguments[ idx ];
if ( !isNumber( val ) || isnan( val ) ) {
throw new TypeError( format( 'invalid argument. Distribution parameter must be a number. Value: `%s`.', val ) );
}
distParams[ i ] = arguments[ idx ];
}
opts = {};
if ( arguments.length > 2 + nDistParams ) {
options = arguments[ 2 + nDistParams ];
err = validate( opts, options );
if ( err ) {
throw err;
}
}
// Make a copy to prevent mutation of x:
x = slice.call( x );
if ( opts.alpha === void 0 ) {
alpha = 0.05;
} else {
alpha = opts.alpha;
}
if ( alpha < 0.0 || alpha > 1.0 ) {
throw new RangeError( format( 'invalid option. `%s` option must be a number on the interval: [0, 1]. Option: `%f`.', 'alpha', alpha ) );
}
// Input data has to be sorted:
if ( opts.sorted !== true ) {
x.sort( ascending );
}
distArgs = [ null ].concat( distParams );
for ( i = 0; i < n; i++ ) {
distArgs[ 0 ] = x[ i ];
yVal = y.apply( null, distArgs );
x[ i ] = yVal - ( i / n );
}
alt = opts.alternative || 'two-sided';
switch ( alt ) {
case 'two-sided':
stat = max( n, [ max( n, x, 1 ), max( n, subtract( 1/n, x ), 1 ) ], 1 );
break;
case 'greater':
stat = max( n, subtract( 1/n, x ), 1 );
break;
case 'less':
stat = max( n, x, 1 );
break;
default:
throw new Error( format( 'invalid option. `%s` option must be one of the following: "%s". Option: `%s`.', 'alternative', [ 'two-sided', 'less', 'greater' ].join( '", "' ), alt ) );
}
if ( alt === 'two-sided' ) {
pval = 1.0 - pKolmogorov( stat, n );
} else {
pval = 1.0 - pKolmogorov1( stat, n );
}
out = {};
setReadOnly( out, 'rejected', pval <= alpha );
setReadOnly( out, 'alpha', alpha );
setReadOnly( out, 'pValue', pval );
setReadOnly( out, 'statistic', stat );
setReadOnly( out, 'method', 'Kolmogorov-Smirnov goodness-of-fit test' );
setReadOnly( out, 'print', print );
setReadOnly( out, 'alternative', alt );
return out;
}
// EXPORTS //
module.exports = kstest;
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