# Documentation

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# wblplot

Weibull probability plot

## Syntax

```wblplot(X) h = wblplot(X) ```

## Description

`wblplot(X)` displays a Weibull probability plot of the data in `X`. If `X` is a matrix, `wblplot` displays a plot for each column. Use a Weibull probability plot to assess visually whether the sample data in `X` comes from a population with a Weibull distribution. If the sample data has a Weibull distribution, then the data appears along the reference line. Distributions other than Weibull can introduce curvature in the plot.

`h = wblplot(X)` returns handles to the plotted lines.

## Examples

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Generate a vector `r` containing 50 random numbers from a Weibull distribution with parameters `A = 1.2` and `B = 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.

```figure; wblplot(r) ```

The plot indicates that the data likely comes from a Weibull distribution.

## Algorithms

`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. In the case of uncensored data, the midpoint is equal to $\frac{\left(i-0.5\right)}{N}$. When the data includes censored observations, use `probplot` instead.

`wblplot` superimposes a reference line to assess the linearity of the plot. The line goes through the first and third quartiles of the data.