# 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

## Functions

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#### Create `WeibullDistribution` Object

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

#### Work with `WeibullDistribution` Object

 `cdf` Cumulative distribution function `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
 `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 Probability Distribution Function Interactive density and distribution plots `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.