median
Median of probability distribution
Syntax
Description
Examples
Median 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);
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]
Compute the median of the fitted distribution.
m = median(pd)
m = 75.0083
For a symmetrical distribution such as the normal distribution, the median is equal to the mean, mu
.
Median 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 median of the distribution.
m = median(pd)
m = 4.1628
For a skewed distribution such as the Weibull distribution, the median and the mean may not be equal.
Calculate the mean of the Weibull distribution and compare it to the median.
mean = mean(pd)
mean = 4.4311
The mean of the distribution is greater than the median.
Plot the pdf to visualize the distribution.
x = [0:.1:15]; pdf = pdf(pd,x); plot(x,pdf)
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
m
— Median
scalar value
Median of the probability distribution, returned as a scalar value. The
value of m
is the 50th percentile of the probability
distribution.
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. Createpd
by fitting a probability distribution to sample data from thefitdist
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
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