Main Content

Normal Distribution

Fit, evaluate, and generate random samples from normal (Gaussian) distribution

Statistics and Machine Learning Toolbox™ offers several ways to work with the normal (Gaussian) distribution.

  • Create a probability distribution object NormalDistribution 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 normal 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 functions can accept parameters of multiple normal distributions.

  • Use the generic distribution functions with the specified distribution name "Normal" and corresponding parameters.

To learn about the normal distribution, see Normal Distribution.


NormalDistributionNormal probability distribution object


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


expand all

Create NormalDistribution Object

makedistCreate probability distribution object
fitdistFit probability distribution object to data

Work with NormalDistribution 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
normcdfNormal cumulative distribution function
normpdfNormal probability density function
norminvNormal inverse cumulative distribution function
normlikeNormal negative loglikelihood
normstatNormal mean and variance
normfitNormal parameter estimates
normrndNormal random numbers
cdfCumulative distribution function
icdfInverse cumulative distribution function
pdfProbability density function
randomRandom numbers
mleMaximum likelihood estimates
histfitHistogram with a distribution fit
normplotNormal probability plot
normspecNormal density plot shading between specifications
plotPlot probability distribution object (Since R2022b)
qqplotQuantile-quantile plot
randtoolInteractive random number generation


  • Normal Distribution

    Learn about the normal distribution. The normal distribution is a two-parameter (mean and standard deviation) family of curves. Central Limit Theorem states that the normal distribution models the sum of independent samples from any distribution as the sample size goes to infinity.