Generalized Pareto probability distribution object
GeneralizedParetoDistribution object consists of
parameters, a model description, and sample data for a generalized Pareto probability
The generalized Pareto distribution is used to model the tails of another distribution. It allows a continuous range of possible shapes that include both the exponential and Pareto distributions as special cases. It has three basic forms, each corresponding to a limiting distribution of exceedance data from a different class of underlying distributions.
Distributions whose tails decrease exponentially, such as the normal, lead to a generalized Pareto shape parameter of zero.
Distributions whose tails decrease polynomially, such as the Student’s t, lead to a positive shape parameter.
Distributions whose tails are finite, such as the beta, lead to a negative shape parameter.
The generalized Pareto distribution uses the following parameters.
|Location (threshold) parameter|
There are several ways to create a
probability distribution object.
k— Shape parameter
Shape parameter for the generalized Pareto distribution, specified as a scalar value.
sigma— Scale parameter
Scale parameter for the generalized Pareto distribution, specified as a nonnegative scalar value.
theta— Location (threshold) parameter
Location (threshold) parameter for the generalized Pareto distribution, specified as a scalar value.
|Cumulative distribution function|
|Gather properties of Statistics and Machine Learning Toolbox object from GPU|
|Inverse cumulative distribution function|
|Mean of probability distribution|
|Median of probability distribution|
|Negative loglikelihood of probability distribution|
|Confidence intervals for probability distribution parameters|
|Probability density function|
|Profile likelihood function for probability distribution|
|Standard deviation of probability distribution|
|Truncate probability distribution object|
|Variance of probability distribution|
Create a generalized Pareto distribution object using the default parameter values.
pd = makedist('GeneralizedPareto')
pd = GeneralizedParetoDistribution Generalized Pareto distribution k = 1 sigma = 1 theta = 1
Create a generalized Pareto distribution object by specifying parameter values.
pd = makedist('GeneralizedPareto','k',0,'sigma',2,'theta',1)
pd = GeneralizedParetoDistribution Generalized Pareto distribution k = 0 sigma = 2 theta = 1
Compute the mean of the distribution.
m = mean(pd)
m = 3
Usage notes and limitations:
GeneralizedParetoDistribution can be a probability distribution object
fitted by using
fitdist with GPU
array input arguments.
The object functions of
GeneralizedParetoDistribution fully support GPU
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).