## Documentation Center |

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

`'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.

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