kstest — Perform a one-sample Kolmogorov-Smirnov test.

kstest(x) performs a one-sample Kolmogorov-Smirnov test of whether the sample in x could come from a standard normal distribution. [h,p,ksstat,cv] = kstest(...) also returns an approximate p-value, the KS statistic, and an approximate critical value.

Syntax

h = kstest(x)
h = kstest(x, Name, Value)
[h, p] = kstest(___)
[h, p, ksstat, cv] = kstest(___)

Inputs

Returns

Returned values from kstest depend on how many outputs the caller requests.

Errors

How kstest works

• kstest(x) requires numeric vector input, omits NaN sample values, and tests against the standard normal CDF.
• kstest(x,"Alpha",alpha) changes the significance level. alpha must be a scalar in (0,1).
• kstest(x,"Tail",tail) accepts "unequal"/"both", "larger", and "smaller".
• kstest(x,"CDF",cdf) accepts a two-column numeric matrix whose first column contains sample points and whose second column contains CDF probabilities in [0,1]. Rows are sorted by sample point, duplicate sample points are collapsed to the largest probability at that point, and probabilities must be nondecreasing after normalization. Sample values must lie inside the table's x range. Values are linearly interpolated between table rows.
• "CDF" also accepts "normcdf", "normal", "norm", or a @normcdf function handle for the standard normal CDF.
• The p-values use standard large-sample approximations. For two-sided tests, cv is returned for Alpha in [0.01,0.20]; for one-sided tests, cv is returned for Alpha in [0.005,0.10]. Outside those ranges, cv is NaN, matching MATLAB's documented critical-value limitations.
• Continuous probability distribution objects for "CDF" are not supported until RunMat's makedist/fitdist distribution object surface exists.
• Typed-integer sample and CDF-table data are RunMat-only extensions. Admitted values must be exactly representable as double before the statistical boundary; integer Alpha has no valid value in the required open interval (0,1) and is rejected.

Examples

Test a centered sample against the standard normal CDF

h = kstest([-1 -0.25 0 0.25 1])

Request all outputs with a one-sided alternative

[h,p,ksstat,cv] = kstest(x, "Tail", "smaller")

Use an explicit CDF table

cdf = [0 0; 0.5 0.5; 1 1];
h = kstest(x, "CDF", cdf)

Using kstest with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how kstest changes the result.

FAQ

Related Stats functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how kstest is executed, line by line, in Rust.

• View the source for kstest in Rust on GitHub
• Learn how the RunMat runtime works
• Found a bug? Open an issue with a minimal reproduction.

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