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(`

creates
a probability plot for the distribution specified by * distribution*,Y)

`distribution`

`distribution`

`'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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