{{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 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 --------