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

Apps

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

Functions

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`WeibullDistribution` Object Functions

Create `WeibullDistribution` Object

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

Work with `WeibullDistribution` Object

`cdf`	Cumulative distribution function
`gather`	Gather properties of Statistics and Machine Learning Toolbox object from GPU
`icdf`	Inverse cumulative distribution function
`iqr`	Interquartile range
`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
`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

Distribution-Specific Functions

`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

Maximum Likelihood Estimation

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

Distribution Plots

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

Topics

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.