@stdlib/stats-kstest
v0.2.2
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One-sample Kolmogorov-Smirnov goodness-of-fit test.
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Kolmogorov-Smirnov Goodness-of-Fit Test
One-sample Kolmogorov-Smirnov goodness-of-fit test.
Installation
npm install @stdlib/stats-kstest
Usage
var kstest = require( '@stdlib/stats-kstest' );
kstest( x, y[, ...params][, opts] )
For a numeric array or typed array
x
, a Kolmogorov-Smirnov goodness-of-fit is computed for the null hypothesis that the values of x
come from the distribution specified by y
. y
can be either a string with the name of the distribution to test against, or a function. In the latter case, y
is expected to be the cumulative distribution function (CDF) of the distribution to test against, with its first parameter being the value at which to evaluate the CDF and the remaining parameters constituting the parameters of the distribution. The parameters of the distribution are passed as additional arguments after y
from kstest
to the chosen CDF. The function returns an object holding the calculated test statistic statistic
and the pValue
of the test.
var factory = require( '@stdlib/random-base-uniform' ).factory;
var runif;
var out;
var x;
var i;
runif = factory( 0.0, 1.0, {
'seed': 8798
});
x = new Array( 100 );
for ( i = 0; i < x.length; i++ ) {
x[ i ] = runif();
}
out = kstest( x, 'uniform', 0.0, 1.0 );
// returns { 'pValue': ~0.703, 'statistic': ~0.069, ... }
The returned object comes with a .print()
method which when invoked will print a formatted output of the hypothesis test results. print
accepts a digits
option that controls the number of decimal digits displayed for the outputs and a decision
option, which when set to false
will hide the test decision.
console.log( out.print() );
/* e.g., =>
Kolmogorov-Smirnov goodness-of-fit test.
Null hypothesis: the CDF of `x` is equal equal to the reference CDF.
pValue: 0.7039
statistic: 0.0689
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
The function accepts the following options
:
- alpha:
number
in the interval[0,1]
giving the significance level of the hypothesis test. Default:0.05
. - alternative: Either
two-sided
,less
orgreater
. Indicates whether the alternative hypothesis is that the true distribution ofx
is not equal to the reference distribution specified byy
(two-sided
), whether it isless
than the reference distribution orgreater
than the reference distribution. Default:two-sided
. - sorted:
boolean
indicating if thex
array is in sorted order (ascending). Default:false
.
By default, the test is carried out at a significance level of 0.05
. To choose a custom significance level, set the alpha
option.
out = kstest( x, 'uniform', 0.0, 1.0, {
'alpha': 0.1
});
console.log( out.print() );
/* e.g., =>
Kolmogorov-Smirnov goodness-of-fit test.
Null hypothesis: the CDF of `x` is equal equal to the reference CDF.
pValue: 0.7039
statistic: 0.0689
Test Decision: Fail to reject null in favor of alternative at 10% significance level
*/
By default, the function tests the null hypothesis that the true distribution of x
and the reference distribution y
are equal to each other against the alternative that they are not equal. To carry out a one-sided hypothesis test, set the alternative
option to either less
or greater
.
var factory = require( '@stdlib/random-base-uniform' ).factory;
var runif;
var out;
var x;
var i;
runif = factory( 0.0, 1.0, {
'seed': 8798
});
x = new Array( 100 );
for ( i = 0; i < x.length; i++ ) {
x[ i ] = runif();
}
out = kstest( x, 'uniform', 0.0, 1.0, {
'alternative': 'less'
});
// returns { 'pValue': ~0.358, 'statistic': ~0.07, ... }
out = kstest( x, 'uniform', 0.0, 1.0, {
'alternative': 'greater'
});
// returns { 'pValue': ~0.907, 'statistic': ~0.02, ... }
To perform the Kolmogorov-Smirnov test, the data has to be sorted in ascending order. If the data in x
are already sorted, set the sorted
option to true
to speed up computation.
x = [ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 ];
out = kstest( x, 'uniform', 0.0, 1.0, {
'sorted': true
});
// returns { 'pValue': ~1, 'statistic': 0.1, ... }
Examples
var kstest = require( '@stdlib/stats-kstest' );
var factory = require( '@stdlib/random-base-normal' ).factory;
var rnorm;
var table;
var out;
var i;
var x;
rnorm = factory({
'seed': 4839
});
// Values drawn from a Normal(3,1) distribution
x = new Array( 100 );
for ( i = 0; i < 100; i++ ) {
x[ i ] = rnorm( 3.0, 1.0 );
}
// Test against N(0,1)
out = kstest( x, 'normal', 0.0, 1.0 );
table = out.print();
/* e.g., returns
Kolmogorov-Smirnov goodness-of-fit test.
Null hypothesis: the CDF of `x` is equal to the reference CDF.
statistic: 0.847
pValue: 0
Test Decision: Reject null in favor of alternative at 5% significance level
*/
// Test against N(3,1)
out = kstest( x, 'normal', 3.0, 1.0 );
table = out.print();
/* e.g., returns
Kolmogorov-Smirnov goodness-of-fit test.
Null hypothesis: the CDF of `x` is equal to the reference CDF.
statistic: 0.0733
pValue: 0.6282
Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
Notice
This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.
Community
License
See LICENSE.
Copyright
Copyright © 2016-2024. The Stdlib Authors.