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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.


WeibullDistributionWeibull probability distribution object


Distribution FitterFit probability distributions to data
Probability Distribution FunctionInteractive density and distribution plots


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Create WeibullDistribution Object

makedistCreate probability distribution object
fitdistFit probability distribution object to data

Work with WeibullDistribution Object

cdfCumulative distribution function
gatherGather properties of Statistics and Machine Learning Toolbox object from GPU (Since R2020b)
icdfInverse cumulative distribution function
iqrInterquartile range of probability distribution
meanMean of probability distribution
medianMedian of probability distribution
negloglikNegative loglikelihood of probability distribution
paramciConfidence intervals for probability distribution parameters
pdfProbability density function
plotPlot probability distribution object (Since R2022b)
proflikProfile likelihood function for probability distribution
randomRandom numbers
stdStandard deviation of probability distribution
truncateTruncate probability distribution object
varVariance of probability distribution
wblcdfWeibull cumulative distribution function
wblpdfWeibull probability density function
wblinvWeibull inverse cumulative distribution function
wbllikeWeibull negative log-likelihood
wblstatWeibull mean and variance
wblfitWeibull parameter estimates
wblrndWeibull random numbers
wblplotWeibull probability plot
mleMaximum likelihood estimates
mlecovAsymptotic covariance of maximum likelihood estimators
distributionFitterOpen Distribution Fitter app
histfitHistogram with a distribution fit
plotPlot probability distribution object (Since R2022b)
qqplotQuantile-quantile plot
randtoolInteractive random number generation
wblplotWeibull 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.