Documentation |
Probability plots
probplot(Y)
probplot(distribution,Y)
probplot(Y,cens,freq)
probplot(ax,Y)
probplot(...,'noref')
probplot(ax,PD)
probplot(ax,fun,params)
h = probplot(...)
probplot(Y) produces a normal probability plot comparing the distribution of the data Y to the normal distribution. Y can be a single vector, or a matrix with a separate sample in each column. The plot includes a reference line useful for judging whether the data follow a normal distribution.
probplot uses midpoint probability plotting positions. The i^{th} sorted value from a sample of size N is plotted against the midpoint in the jump of the empirical CDF on the y axis. With uncensored data, that midpoint is (i–0.5)/N. With censored data (see below), the y value is more complicated to compute.
probplot(distribution,Y) creates a probability plot for the distribution specified by distribution. Acceptable strings for distribution are:
'exponential' — Exponential probability plot (nonnegative values)
'extreme value' — Extreme value probability plot (all values)
'lognormal' — Lognormal probability plot (positive values)
'normal' — Normal probability plot (all values)
'rayleigh' — Rayleigh probability plot (positive values)
'weibull' — Weibull probability plot (positive values)
The y axis scale is based on the selected distribution. The x axis has a log scale for the Weibull and lognormal distributions, and a linear scale for the others.
Not all distributions are appropriate for all data sets, and probplot will error when asked to create a plot with a data set that is inappropriate for a specified distribution. Appropriate data ranges for each distribution are given parenthetically in the list above.
probplot(Y,cens,freq) or probplot(distname,Y,cens,freq) requires a vector Y. cens is a vector of the same size as Y and contains 1 for observations that are right-censored and 0 for observations that are observed exactly. freq is a vector of the same size as Y, containing integer frequencies for the corresponding elements in Y.
probplot(ax,Y) takes a handle ax to an existing probability plot, and adds additional lines for the samples in Y. ax is a handle for a set of axes.
probplot(...,'noref') omits the reference line.
probplot(ax,PD) takes a probability distribution object, PD, and adds a fitted line to the axes specified by ax to represent the probability distribution specified by PD. PD is a ProbDist object of the ProbDistUnivParam class or ProbDistUnivKernel class.
probplot(ax,fun,params) takes a function fun and a set of parameters, params, and adds fitted lines to the axes of an existing probability plot specified by ax. fun is a function handle to a cdf function, specified with @ (for example, @wblcdf). params is the set of parameters required to evaluate fun, and is specified as a cell array or vector. The function must accept a vector of X values as its first argument, then the optional parameters, and must return a vector of cdf values evaluated at X.
h = probplot(...) returns handles to the plotted lines.