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 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 distribution-specific functions can accept parameters of multiple normal distributions.
Use generic distribution functions (cdf, icdf, pdf, random) with a specified distribution name ('Normal') and parameters.

To learn about the normal distribution, see Normal Distribution.

Objects

NormalDistribution Normal probability distribution object

Apps

Distribution Fitter	Fit probability distributions to data
Probability Distribution Function	Interactive density and distribution plots

Functions

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`NormalDistribution` Object Functions

Create `NormalDistribution` Object

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

Work with `NormalDistribution` 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

Distribution-Specific Functions

`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

Maximum Likelihood Estimation

`mle`	Maximum likelihood estimates
`mlecov`	Asymptotic covariance of maximum likelihood estimators

Distribution Plots

`histfit`	Histogram with a distribution fit
`normplot`	Normal probability plot
`normspec`	Normal density plot shading between specifications
`qqplot`	Quantile-quantile plot
`randtool`	Interactive random number generation

Topics

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.