Weibull Distribution

Fit, evaluate, and generate random samples from Weibull distribution

Statistics and Machine Learning Toolbox™ offers several ways to work with the Weibull distribution.

Create a probability distribution object WeibullDistribution by fitting a probability distribution to sample data or by specifying parameter values. Then, use object functions to evaluate the distribution, generate random numbers, and so on.
Work with the Weibull distribution interactively by using the Distribution Fitter app. You can export an object from the app and use the object functions.
Use distribution-specific functions with specified distribution parameters. The distribution-specific functions can accept parameters of multiple Weibull distributions.
Use generic distribution functions (cdf, icdf, pdf, random) with a specified distribution name ('Weibull') and parameters.

To learn about the Weibull distribution, see Weibull Distribution.

Objects

WeibullDistribution Weibull probability distribution object

Distribution Fitter	Fit probability distributions to data
Probability Distribution Function	Interactive density and distribution plots

`makedist`	Create probability distribution object
`fitdist`	Fit probability distribution object to data

`cdf`	Cumulative distribution function
`gather`	Gather properties of Statistics and Machine Learning Toolbox object from GPU (Since R2020b)
`icdf`	Inverse cumulative distribution function
`iqr`	Interquartile range of probability distribution
`mean`	Mean of probability distribution
`median`	Median of probability distribution
`negloglik`	Negative loglikelihood of probability distribution
`paramci`	Confidence intervals for probability distribution parameters
`pdf`	Probability density function
`plot`	Plot probability distribution object (Since R2022b)
`proflik`	Profile likelihood function for probability distribution
`random`	Random numbers
`std`	Standard deviation of probability distribution
`truncate`	Truncate probability distribution object
`var`	Variance of probability distribution

`wblcdf`	Weibull cumulative distribution function
`wblpdf`	Weibull probability density function
`wblinv`	Weibull inverse cumulative distribution function
`wbllike`	Weibull negative log-likelihood
`wblstat`	Weibull mean and variance
`wblfit`	Weibull parameter estimates
`wblrnd`	Weibull random numbers
`wblplot`	Weibull probability plot

`mle`	Maximum likelihood estimates
`mlecov`	Asymptotic covariance of maximum likelihood estimators

`distributionFitter`	Open Distribution Fitter app
`histfit`	Histogram with a distribution fit
`plot`	Plot probability distribution object (Since R2022b)
`qqplot`	Quantile-quantile plot
`randtool`	Interactive random number generation
`wblplot`	Weibull probability plot

Weibull Distribution
The Weibull pdf is an appropriate analytical tool for modeling the breaking strength of materials. Current usage also includes reliability and lifetime modeling.
Three-Parameter Weibull Distribution
Find maximum likelihood estimates (MLEs) for the three-parameter Weibull distribution with scale, shape, and location parameters.