var

Variance of probability distribution

Syntax

v = var(pd)

Description

v = var(pd) returns the variance v of the probability distribution pd.

Examples

Variance of a Fitted Distribution

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

load examgrades
x = grades(:,1);

Fit a normal distribution object 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]

Compute the variance of the fitted distribution.

v = var(pd)

v = 
76.0419

For a normal distribution, the variance is equal to the square of the parameter sigma.

Variance of Skewed Distribution

Create a Weibull probability distribution object.

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

pd = 
  WeibullDistribution

  Weibull distribution
    A = 5
    B = 2

Compute the variance of the distribution.

v = var(pd)

v = 
5.3650

Variance of Triangular Distribution

Create a triangular distribution object.

pd = makedist('Triangular','A',-3,'B',1,'C',3)

pd = 
  TriangularDistribution

A = -3, B = 1, C = 3

Compute the variance of the distribution.

v = var(pd)

v = 
1.5556

Variance of a Kernel Distribution

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

load examgrades;
x = grades(:,1);

Fit a kernel distribution object to the data.

pd = fitdist(x,'Kernel')

pd = 
  KernelDistribution

    Kernel = normal
    Bandwidth = 3.61677
    Support = unbounded

Compute the variance of the fitted distribution.

v = var(pd)

v = 
88.4893

Input Arguments

pd — Probability distribution

probability distribution object

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

Distribution Object	Function or App Used 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

v — Variance

nonnegative scalar value

Variance of the probability distribution, returned as a nonnegative 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.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2013a