time-to-botec/squiggle/node_modules/@stdlib/stats/kstest/docs/repl.txt

{{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
    --------