Weibull probability plot
wblplot( creates a Weibull probability
plot comparing the distribution of the data in
x to the Weibull
wblplot plots each data point in
using plus sign (
'+') markers and draws two reference lines that
represent the theoretical distribution. A solid reference line connects the first
and third quartiles of the data, and a dashed reference line extends the solid line
to the ends of the data. If the sample data has a Weibull distribution, then the
data points appear along the reference line. A distribution other than Weibull
introduces curvature in the data plot.
graphics handles corresponding to the plotted lines, using any of the input
arguments in the previous syntaxes.
h = wblplot(___)
Create Weibull Probability Plot
Generate a vector
r containing 50 random numbers from the Weibull distribution with the scale parameter 1.2 and the shape parameter 1.5.
rng('default') % For reproducibility r = wblrnd(1.2,1.5,50,1);
Create a Weibull probability plot to visually determine if the data comes from a Weibull distribution.
The plot indicates that the data likely comes from a Weibull distribution.
Test for Weibull Distribution
Generate two sample data sets, one from a Weibull distribution and another from a lognormal distribution. Perform the Lilliefors test to assess whether each data set is from a Weibull distribution. Confirm the test decision by performing a visual comparison using a Weibull probability plot (
Generate samples from a Weibull distribution.
rng('default') data1 = wblrnd(0.5,2,[500,1]);
Perform the Lilliefors test by using the
lillietest. To test data for a Weibull distribution, test if the logarithm of the data has an extreme value distribution.
h1 = lillietest(log(data1),'Distribution','extreme value')
h1 = 0
The returned value of
h1 = 0 indicates that
lillietest fails to reject the null hypothesis at the default 5% significance level. Confirm the test decision using a Weibull probability plot.
The plot indicates that the data follows a Weibull distribution.
Generate samples from a lognormal distribution.
Perform the Lilliefors test.
h2 = lillietest(log(data2),'Distribution','extreme value')
h2 = 1
The returned value of
h2 = 1 indicates that
lillietest rejects the null hypothesis at the default 5% significance level. Confirm the test decision using a Weibull probability plot.
The plot indicates that the data does not follow a Weibull distribution.
x — Sample data
numeric vector | numeric matrix
Sample data, specified as a numeric vector or numeric matrix.
displays each value in
x using the symbol
x is a matrix, then
wblplot displays a
separate line for each column of
h — Graphics handles for line objects
Line graphics handles
Graphics handles for line objects, returned as a vector of
graphics handles. Graphics handles are unique identifiers that you can use to query and
modify the properties of a specific line on the plot. For each column of
wblplot returns three
The line representing the data points.
wblplotrepresents each data point in
xusing plus sign (
The line joining the first and third quartiles of each column of
x, represented as a solid line.
The extrapolation of the quartile line, extended to the minimum and maximum values of
x, represented as a dashed line.
To view and set properties of line objects, use dot notation. For information on using
dot notation, see Access Property Values. For
information on the
Line properties that you can set, see Line Properties.
wblplot matches the quantiles of sample data to the quantiles of
a Weibull distribution. The sample data is sorted, scaled logarithmically, and plotted
on the x-axis. The y-axis represents the quantiles of the Weibull distribution,
converted into probability values. Therefore, the y-axis scaling is not linear.
Where the x-axis value is the ith sorted value from a sample of size N, the y-axis value is the midpoint between evaluation points of the empirical cumulative distribution function of the data. The midpoint is equal to .
wblplot superimposes a reference line to assess the linearity of
the plot. The line goes through the first and third quartiles of the data.
You can use the
probplot function to create a probability
probplot function enables you to indicate censored data
and specify the distribution for a probability plot.