mean

Mean of probability distribution

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Syntax

m = mean(pd)

Description

example

m = mean(pd) returns the mean m of the probability distribution pd.

Examples

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Mean of Fitted Distribution

Open Live Script

Load the sample data. Create a vector containing the first column of students’ exam grade data.

load examgrades
x = grades(:,1);

Create a normal distribution object by fitting it to the data.

pd = fitdist(x,'Normal')

pd = 
  NormalDistribution

  Normal distribution
       mu = 75.0083   [73.4321, 76.5846]
    sigma =  8.7202   [7.7391, 9.98843]

The distribution object display includes the parameter estimates for the mean (mu) and standard deviation (sigma), and the 95% confidence intervals for the parameters.

Compute the mean of the fitted distribution.

m = mean(pd)

m = 75.0083

The mean of the normal distribution is equal to the parameter mu.

Mean of Skewed Distribution

Open Live Script

Create a Weibull probability distribution object.

pd = makedist('Weibull','A',5,'B',2)

pd = 
  WeibullDistribution

  Weibull distribution
    A = 5
    B = 2

Compute the mean of the distribution.

mean = mean(pd)

mean = 4.4311

Mean of a Uniform Distribution

Open Live Script

Create a uniform distribution object

pd = makedist('Uniform','lower',-3,'upper',5)

pd = 
  UniformDistribution

  Uniform distribution
    Lower = -3
    Upper =  5

Compute the mean of the distribution.

m = mean(pd)

m = 1

Mean of a Kernel Distribution

Open Live Script

Load the sample data. Create a probability distribution object by fitting a kernel distribution to the miles per gallon (MPG) data.

load carsmall;
pd = fitdist(MPG,'Kernel')

pd = 
  KernelDistribution

    Kernel = normal
    Bandwidth = 4.11428
    Support = unbounded

Compute the mean of the distribution.

mean(pd)

ans = 23.7181

Input Arguments

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`pd` — Probability distribution
probability distribution object

Probability distribution, specified as one of the probability distribution objects in this table.

Distribution Object	Function or App to Create Probability Distribution Object
`BetaDistribution`	`makedist`, `fitdist`, Distribution Fitter
`BinomialDistribution`	`makedist`, `fitdist`, Distribution Fitter
`BirnbaumSaundersDistribution`	`makedist`, `fitdist`, Distribution Fitter
`BurrDistribution`	`makedist`, `fitdist`, Distribution Fitter
`ExponentialDistribution`	`makedist`, `fitdist`, Distribution Fitter
`ExtremeValueDistribution`	`makedist`, `fitdist`, Distribution Fitter
`GammaDistribution`	`makedist`, `fitdist`, Distribution Fitter
`GeneralizedExtremeValueDistribution`	`makedist`, `fitdist`, Distribution Fitter
`GeneralizedParetoDistribution`	`makedist`, `fitdist`, Distribution Fitter
`HalfNormalDistribution`	`makedist`, `fitdist`, Distribution Fitter
`InverseGaussianDistribution`	`makedist`, `fitdist`, Distribution Fitter
`KernelDistribution`	`fitdist`, Distribution Fitter
`LogisticDistribution`	`makedist`, `fitdist`, Distribution Fitter
`LoglogisticDistribution`	`makedist`, `fitdist`, Distribution Fitter
`LognormalDistribution`	`makedist`, `fitdist`, Distribution Fitter
`LoguniformDistribution`	`makedist`
`MultinomialDistribution`	`makedist`
`NakagamiDistribution`	`makedist`, `fitdist`, Distribution Fitter
`NegativeBinomialDistribution`	`makedist`, `fitdist`, Distribution Fitter
`NormalDistribution`	`makedist`, `fitdist`, Distribution Fitter
`PiecewiseLinearDistribution`	`makedist`
`PoissonDistribution`	`makedist`, `fitdist`, Distribution Fitter
`RayleighDistribution`	`makedist`, `fitdist`, Distribution Fitter
`RicianDistribution`	`makedist`, `fitdist`, Distribution Fitter
`StableDistribution`	`makedist`, `fitdist`, Distribution Fitter
`tLocationScaleDistribution`	`makedist`, `fitdist`, Distribution Fitter
`TriangularDistribution`	`makedist`
`UniformDistribution`	`makedist`
`WeibullDistribution`	`makedist`, `fitdist`, Distribution Fitter

Output Arguments

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`m` — Mean
scalar value

Mean of the probability distribution, returned as a scalar value.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

The input argument pd can be a fitted probability distribution object for beta, exponential, extreme value, lognormal, normal, and Weibull distributions. Create pd by fitting a probability distribution to sample data from the fitdist function. For an example, see Code Generation for Probability Distribution Objects.

For more information on code generation, see Introduction to Code Generation and General Code Generation Workflow.