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.

Objects

NormalDistribution Normal probability distribution object

Fit probability distributions to data

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

`cdf`	Cumulative distribution function
`gather`	Gather properties of Statistics and Machine Learning Toolbox object from GPU (Since R2020b)
`icdf`	Inverse cumulative distribution function
`iqr`	Interquartile range of probability distribution
`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
`plot`	Plot probability distribution object (Since R2022b)
`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

`normcdf`	Normal cumulative distribution function
`normpdf`	Normal probability density function
`norminv`	Normal inverse cumulative distribution function
`normlike`	Normal negative loglikelihood
`normstat`	Normal mean and variance
`normfit`	Normal parameter estimates
`normrnd`	Normal random numbers

`cdf`	Cumulative distribution function
`icdf`	Inverse cumulative distribution function
`pdf`	Probability density function
`random`	Random numbers
`mle`	Maximum likelihood estimates

`histfit`	Histogram with a distribution fit
`normplot`	Normal probability plot
`normspec`	Normal density plot shading between specifications
`plot`	Plot probability distribution object (Since R2022b)
`qqplot`	Quantile-quantile plot
`disttool`	Interactive density and distribution plots
`randtool`	Interactive 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.