Statistics in the command window#

Every name on this page is typed at the command window (or passed to ICoreBlocks --console "<line>") and answers what MATLAB's Statistics and Machine Learning Toolbox answers for the same arguments — same parameter order, same defaults, same tie and edge rules. This is the largest of the toolbox families here: 190 names, covering the distributions, the descriptive statistics, the classical tests, regression, and the numeric-in/numeric-out half of clustering and multivariate analysis.

What is here is everything that takes numbers and answers numbers. What is NOT here is everything that answers an OBJECT — fitlm, fitcsvm, makedist, cvpartition and the rest of the model classes — because this console has no object types. The last section says what to reach for instead.

The families, and what to reach for#

The nineteen distribution families#

Each family has the same five or six spellings, and they mean the same thing in every one: pdf the density, cdf the cumulative probability, inv the quantile, rnd a DRAW, stat the mean and VARIANCE as [m, v], and fit the maximum-likelihood estimate with its confidence interval. <name>cdf takes a trailing "upper" for the upper tail computed exactly rather than as 1 - p.

Four families answer a fit this console does not have — beta, negative binomial and the two generalized ones — and those refuse by name; their densities, cumulatives, quantiles and draws are all here. mle(x, "Distribution", name) reaches the fits it does have under one name.

A worked line or two#

The normal family, and a sample summarised:

>>> [normpdf(1), normcdf(1), norminv(0.975)]
[[0.241971, 0.841345, 1.95996]]  # Matrix of Double

>>> x = [2.1, 3.4, 1.9, 4.2, 2.8, 3.1, 2.5, 3.9]; [mean(x), std(x), prctile(x, 75), iqr(x)]
[[2.9875, 0.82191, 3.65, 1.35]]  # Matrix of Double

A one-sample t-test against a hypothesised mean, and the same data fitted with its exact intervals:

>>> x = [2.1, 3.4, 1.9, 4.2, 2.8, 3.1, 2.5, 3.9]; [h, p, ci] = ttest(x, 2.5)
h = 0  # Integer
p = 0.137319  # Double
ci = [[2.30037, 3.67463]]  # Matrix of Double

>>> x = [2.1, 3.4, 1.9, 4.2, 2.8, 3.1, 2.5, 3.9]; [muhat, sigmahat, muci, sigmaci] = normfit(x)
muhat = 2.9875  # Double
sigmahat = 0.82191  # Double
muci = [[2.30037], [3.67463]]  # Matrix of Double
sigmaci = [[0.543426], [1.67281]]  # Matrix of Double

Regression, correlation with its p-value, and principal components:

>>> X = [1 2; 2 3; 3 5; 4 4; 5 7]; y = [2; 3; 5; 4; 8]; regress(y, [ones(5,1), X])
[[-0.6], [-0.0444444], [1.22222]]  # Matrix of Double

>>> x = [1 2 3 4 5]; y = [2 4 5 4 5]; [rho, pval] = corr(x', y')
rho = 0.774597  # Double
pval = 0.124027  # Double

>>> X = [1 2; 2 3; 3 5; 4 4; 5 7]; [coeff, score, latent] = pca(X); latent'
[[5.91469, 0.285306]]  # Matrix of Double

Distances and clustering, with the start pinned so the answer is reproducible:

>>> D = pdist([1 1; 2 2; 4 5]); [D; squareform(D)]
[[1.41421, 5, 3.60555], [0, 1.41421, 5], [1.41421, 0, 3.60555], [5, 3.60555, 0]]  # Matrix of Double

>>> X = [1 1; 1.5 2; 3 4; 5 7; 3.5 5; 4.5 5; 3.5 4.5]; [idx, C] = kmeans(X, 2, "Start", [1 1; 5 7])
idx = [[1], [1], [2], [2], [2], [2], [2]]  # Matrix of Double
C = [[1.25, 1.5], [3.9, 5.1]]  # Matrix of Double

Every transcript on this page is real output, captured with ICoreBlocks --console "<line>" on 2026-09-05 at commit bd974745.

Ten things that surprise people#

1. ttest(x, y) with two VECTORS is the PAIRED test. The same subjects measured twice, n - 1 degrees of freedom. The unpaired one is ttest2. Nothing in either call says which is which, and they answer different p-values for the same pair.

2. pdf("normal", 1) is NaN where normpdf(1) is 0.242. The generic, string-named forms read an omitted parameter as ZERO, not as the family's default — MATLAB's pdf.m does if nargin < 3, a = 0; end, and a normal density with sigma 0 is NaN. random does not zero-fill at all; it forwards its arguments, so random("normal") is an error on both sides:

   `` >>> [pdf("normal", 1), normpdf(1)] [[NaN, 0.241971]] # Matrix of Double ``

3. wblpdf's parameters are (SCALE, SHAPE) — wblpdf(x, A, B) has A the scale and B the exponent, the reverse of the (k, λ) most textbooks write.
4. ridge's default answer is not on your data's scale and has no intercept. ridge(y, X, k) and ridge(y, X, k, 1) are the same call: both answer p coefficients for the centred, SCALED design. Only ridge(y, X, k, 0) divides back by the column deviations and prepends the intercept — so the two forms differ in SIZE as well as in value.
5. robustfit ADDS a constant column; regress never does. Two neighbouring functions with opposite conventions. Pass "off" as robustfit's fifth argument to stop it.
6. silhouette's default metric is SQUARED Euclidean, not Euclidean. It is the one place in this toolbox where a squared distance is the default, and it moves every number.
7. runstest's default reference is the MEAN, not the median, and values exactly equal to it are DROPPED before any run is counted.
8. cluster(Z, "MaxClust", k) cuts by DISTANCE, not by the inconsistency its documentation calls the default. MATLAB's cluster.m rewrites the criterion whenever no cutoff was given and none was named; reproduced here.
9. lasso's B comes back in ASCENDING lambda order, on the ORIGINAL scale of X, and the sequence can be shorter than you asked for. The fit runs downward from lambdaMax and reverses at the end, and it stops early once it passes DFmax or its error falls below a thousandth of the null model's. It also standardises with the POPULATION deviation where ridge uses the sample one.
10. Anything that DRAWS cannot be compared to MATLAB and does not pretend to be. normrnd, random, bootstrp, datasample, kmeans without a "Start" — MATLAB's stream is a Mersenne Twister and this console's is not, so the same seed gives different numbers and no seed makes them agree. The translation is sound; the values are the sampler's. Pin the start, or compare a statistic of the draw rather than the draw.

What is not here#

Refused, with the reason in the message — the common shape is a result that MATLAB returns as a STRUCT or a CELL, which this console has no kind for:

• anova1's table and stats, chi2gof's third output, runstest's third, robustfit's stats, lasso's FitInfo — every one of these refuses by name rather than being quietly absent, and says which rule it met.
• corr's Spearman and Kendall p-values (the correlations themselves are here). MATLAB reaches those two through a permutation distribution in compiled code.
• nlpredci's simultaneous OBSERVATION interval — its Scheffé parameter is chosen by an unpublished rule.
• rotatefactors on an ALREADY-rotated loading matrix, which restarts MATLAB from a random orthogonal matrix.
• runstest(..., "ud"), which needs a shipped data file.

Not known to the console at all — typing one of these answers unknown function '<name>':

Four names on this console are core MATLAB's rather than the toolbox's, and so carry no toolbox tag even though MATLAB puts them here: rms, prctile, quantile and iqr. They work the same way; the tag only says whether a licence would be needed on the other side.

Where to look next#

• Command glossary — console commands, verbs, functions — every name the console answers, grouped by toolbox, with each one's arguments.
• The command window — the command engine for a user — the engine itself: variables, multiple outputs, scripts, and running a line headlessly.
• Curve fitting in the command window — fit and its model library, for fitting a curve rather than testing a hypothesis.
• Numerics — what the solver will and will not do — what a double can carry, and where these answers stop being exact.