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{{alias}}( x, y[, ...params][, options] )
Computes a Kolmogorov-Smirnov goodness-of-fit test.
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.
The returned object comes with a `.print()` method which when invoked will
print a formatted output of the hypothesis test results.
Parameters
----------
x: Array<number>
Input array holding numeric values.
y: Function|string
Either a CDF function or a string denoting the name of a distribution.
params: ...number (optional)
Distribution parameters passed to reference CDF.
options: Object (optional)
Function options.
options.alpha: number (optional)
Number in the interval `[0,1]` giving the significance level of the
hypothesis test. Default: `0.05`.
options.sorted: boolean (optional)
Boolean indicating if the input array is already in sorted order.
Default: `false`.
options.alternative: string (optional)
Either `two-sided`, `less` or `greater`. Indicates whether the
alternative hypothesis is that the true distribution of `x` is not equal
to the reference distribution specified by `y` (`two-sided`), whether it
is `less` than the reference distribution or `greater` than the
reference distribution. Default: `'two-sided'`.
Returns
-------
out: Object
Test result object.
out.alpha: number
Used significance level.
out.rejected: boolean
Test decision.
out.pValue: number
p-value of the test.
out.statistic: number
Value of test statistic.
out.alternative: string
Used test alternative. Either `two-sided`, `less` or `greater`.
out.method: string
Name of test.
out.print: Function
Function to print formatted output.
Examples
--------
// Verify that data is drawn from a normal distribution:
> var rnorm = {{alias:@stdlib/random/base/normal}}.factory({ 'seed': 4839 });
> var x = new Array( 100 );
> for ( var i = 0; i < 100; i++ ) { x[ i ] = rnorm( 3.0, 1.0 ); }
// Test against N(0,1)
> var out = {{alias}}( x, 'normal', 0.0, 1.0 )
{ pValue: 0.0, statistic: 0.847, ... }
// Test against N(3,1)
> out = {{alias}}( x, 'normal', 3.0, 1.0 )
{ pValue: 0.6282, statistic: 0.0733, ... }
// Verify that data is drawn from a uniform distribution:
> runif = {{alias:@stdlib/random/base/uniform}}.factory( 0.0, 1.0, { 'seed': 8798 })
> x = new Array( 100 );
> for ( i = 0; i < x.length; i++ ) { x[ i ] = runif(); }
> out = {{alias}}( x, 'uniform', 0.0, 1.0 )
{ pValue: ~0.703, statistic: ~0.069, ... }
// Print output:
> out.print()
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
// Set custom significance level:
> out = {{alias}}( x, 'uniform', 0.0, 1.0, { 'alpha': 0.1 })
{ pValue: ~0.7039, statistic: ~0.069, ... }
// Carry out one-sided hypothesis tests:
> runif = {{alias:@stdlib/random/base/uniform}}.factory( 0.0, 1.0, { 'seed': 8798 });
> x = new Array( 100 );
> for ( i = 0; i < x.length; i++ ) { x[ i ] = runif(); }
> out = {{alias}}( x, 'uniform', 0.0, 1.0, { 'alternative': 'less' })
{ pValue: ~0.358, statistic: ~0.07, ... }
> out = {{alias}}( x, 'uniform', 0.0, 1.0, { 'alternative': 'greater' })
{ pValue: ~0.907, statistic: ~0.02, ... }
// Set `sorted` option to true when data is in increasing order:
> x = [ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 ];
> out = {{alias}}( x, 'uniform', 0.0, 1.0, { 'sorted': true })
{ pValue: ~1, statistic: 0.1, ... }
See Also
--------
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