GeneralizedParetoDistribution
Generalized Pareto probability distribution object.
A GeneralizedParetoDistribution object consists of parameters, a
model description, and sample data for a generalized Pareto probability
distribution.
The generalized Pareto distribution uses the following parameters.
| Parameter | Description | Support |
|---|---|---|
k | Shape | |
sigma | Scale | |
theta | Location |
There are several ways to create a GeneralizedParetoDistribution object.
fitdist function.
makedist function.
GeneralizedParetoDistribution (k, sigma)
to create a generalized Pareto distribution with specified parameter values.
GeneralizedParetoDistribution.fit (x,
k, freq) to a distribution to data x.
It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the
constructor and the aforementioned static method.
A GeneralizedParetoDistribution object contains the following
properties, which can be accessed using dot notation.
DistributionName | DistributionCode | NumParameters | ParameterNames |
ParameterDescription | ParameterValues | ParameterValues | ParameterCI |
ParameterIsFixed | Truncation | IsTruncated | InputData |
A GeneralizedParetoDistribution object contains the following methods:
cdf, icdf, iqr, mean, median,
negloglik, paramci, pdf, plot, proflik,
random, std, truncate, var.
Further information about the generalized Pareto distribution can be found at https://en.wikipedia.org/wiki/Generalized_Pareto_distribution
See also: fitdist, makedist, gpcdf, gpinv, gppdf, gprnd, gpfit, gplike, gpstat
Source Code: GeneralizedParetoDistribution
cdf
Compute the inverse cumulative distribution function (iCDF).
p = icdf (pd, x) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in x.
icdf
Compute the inverse cumulative distribution function (iCDF).
p = icdf (pd, x) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in x.
iqr
Compute the interquartile range of a probability distribution.
r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.
mean
Compute the mean of a probability distribution.
m = mean (pd) computes the mean of the probability
distribution object, pd.
median
Compute the median of a probability distribution.
m = median (pd) computes the median of the probability
distribution object, pd.
negloglik
Compute the negative loglikelihood of a probability distribution.
m = negloglik (pd) computes the negative loglikelihood
of the probability distribution object, pd.
paramci
Compute the confidence intervals for probability distribution parameters.
ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.
ci = paramci (pd, Name, Value) computes the
confidence intervals with additional options specified specified by
Name-Value pair arguments listed below.
| Name | Value | |
|---|---|---|
"Alpha" | A scalar value in the range specifying the significance level for the confidence interval. The default value 0.05 corresponds to a 95% confidence interval. | |
"Parameter" | A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters. |
paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.
pdf
Compute the probability distribution function (PDF).
y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.
plot
Plot a probability distribution object.
plot (pd plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.
plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.
| Name | Value | |
|---|---|---|
"PlotType" | A character vector specifying the plot
type. "pdf" plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. "cdf" plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
"probability" plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data. | |
"Discrete" | A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored. | |
"Parent" | An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist. |
h = plot (…) returns a graphics handle to the plotted
objects.
proflik
"Display", display)"Display", display)Profile likelihood function for a probability distribution object.
[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 95% confidence interval and computes
100 equispaced values for the selected parameter. pd must be
fitted to data.
[nlogL, param] = proflik (pd, pnum,
also plots the profile likelihood
against the default range of the selected parameter.
"Display", "on")
[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.
[nlogL, param] = proflik (pd, pnum,
setparam, also plots the profile
likelihood against the user-defined range of the selected parameter.
"Display", "on")
For the generalized Pareto distribution, pnum = 1 selects
the parameter k, pnum = 2 selects the parameter
sigma, and pnum = 3 selects the parameter theta.
When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.
random
Generate random arrays from the probability distribution object.
r = random (pd) returns a random number from the
distribution object pd.
When called with a single size argument, betarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.
std
Compute the standard deviation of a probability distribution.
s = std (pd) computes the standard deviation of the
probability distribution object, pd.
truncate
Truncate a probability distribution.
t = truncate (pd) returns a probability distribution
t, which is the probability distribution pd truncated to the
specified interval with lower limit, lower, and upper limit,
upper. If pd is fitted to data with fitdist, the
returned probability distribution t is not fitted, does not contain
any data or estimated values, and it is as it has been created with the
makedist function, but it includes the truncation interval.
var
Compute the variance of a probability distribution.
v = var (pd) computes the standard deviation of the
probability distribution object, pd.