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Exponential Distribution

Fit, evaluate, and generate random samples from exponential distribution

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

  • Create a probability distribution object ExponentialDistribution 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 exponential 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 exponential distributions.

  • Use generic distribution functions (cdf, icdf, pdf, random) with a specified distribution name ('Exponential') and parameters.

To learn about the exponential distribution, see Exponential Distribution.


ExponentialDistributionExponential probability distribution object


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


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Create ExponentialDistribution Object

makedistCreate probability distribution object
fitdistFit probability distribution object to data

Work with ExponentialDistribution 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
expcdfExponential cumulative distribution function
exppdfExponential probability density function
expinvExponential inverse cumulative distribution function
explikeExponential negative log-likelihood
expstatExponential mean and variance
expfitExponential parameter estimates
exprndExponential random numbers
mleMaximum likelihood estimates
distributionFitterOpen Distribution Fitter app
histfitHistogram with a distribution fit
plotPlot probability distribution object (Since R2022b)
qqplotQuantile-quantile plot
randtoolInteractive random number generation


  • Exponential Distribution

    The exponential distribution is special because of its utility in modeling events that occur randomly over time. The main application area is in studies of lifetimes.