26.3 Statistical Plots

Octave can create Quantile Plots (QQ-Plots), and Probability Plots (PP-Plots). These are simple graphical tests for determining if a data set comes from a certain distribution.

Note that Octave can also show histograms of data using the hist function as described in Two-Dimensional Plots.

: [q, s] = qqplot (x)

: [q, s] = qqplot (x, y)

: [q, s] = qqplot (x, dist)

: [q, s] = qqplot (x, y, params)

: qqplot (…)

Perform a QQ-plot (quantile plot).

If F is the CDF of the distribution dist with parameters params and G its inverse, and x a sample vector of length n, the QQ-plot graphs ordinate s(i) = i-th largest element of x versus abscissa q(if) = G((i - 0.5)/n).

If the sample comes from F, except for a transformation of location and scale, the pairs will approximately follow a straight line.

If the second argument is a vector y the empirical CDF of y is used as dist.

The default for dist is the standard normal distribution. The optional argument params contains a list of parameters of dist. For example, for a quantile plot of the uniform distribution on [2,4] and x, use

qqplot (x, "unif", 2, 4)

dist can be any string for which a function distinv or dist_inv exists that calculates the inverse CDF of distribution dist.

If no output arguments are given, the data are plotted directly.

: [p, y] = ppplot (x, dist, params)

Perform a PP-plot (probability plot).

If F is the CDF of the distribution dist with parameters params and x a sample vector of length n, the PP-plot graphs ordinate y(i) = F (i-th largest element of x) versus abscissa p(i) = (i - 0.5)/n. If the sample comes from F, the pairs will approximately follow a straight line.

The default for dist is the standard normal distribution.

The optional argument params contains a list of parameters of dist.

For example, for a probability plot of the uniform distribution on [2,4] and x, use

ppplot (x, "uniform", 2, 4)

dist can be any string for which a function dist_cdf that calculates the CDF of distribution dist exists.

If no output is requested then the data are plotted immediately.