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![]() | Testing Menu | ![]() | ![]() | Options Menu |
Simulate Menu
The Simulate Menu provides options to simulate the distribution
and the MSE/Bias of the estimators provided in the menu system.
The following options are available:
MAX domain: Distribution of Estimator MSE/Bias of Estimator POT domain: Distribution of Estimator MSE/Bias of Estimator
Distribution of Estimator (POT)
Select a df with shape parameter gamma (or likewise, with
shape parameter alpha) by entering its qf in the
edit field on the right-hand side. Use the
predefined function calls provided by the
UserFormula facility and XPL. For example, enter
paretoqf(2,x) to
generate standard Pareto data under the shape parameter alpha=2.
In the edit field below, enter the true parameter value for
alpha or gamma.
Xtremes needs this information to center the data.
Next, select an estimator on the left-hand
side. Then enter values for sample
size n, number of extremes k and number of simulations N. A set of
estimates of gamma, say gamma(k,n,1), ..., gamma(k,n,N), is
generated and written to a file of type Xtremes Univariate Data.
The distribution of the estimator gamma[k,n] may be visualized by
means of procedures in the Visualize menu or in the SUM domain
(the same holds for sets of estimators for alpha as well):
MSE/Bias of Estimator (POT)
A Monte Carlo Simulation is carried out to estimate the mean squared
error (MSE) and the bias of estimators.
Select a df with shape parameter gamma (or likewise, with
shape parameter alpha) by entering its qf in the
edit field on the right-hand side. Use the
predefined function calls provided by the
UserFormula facility and XPL. For example, enter
paretoqf(2,x) to
generate standard Pareto data under the shape parameter alpha=2. In
the edit field below, enter the true parameter value for alpha
or gamma.
Xtremes requires this information to calculate MSE and bias.
Next, select an estimator on the left-hand side and enter values for sample size n, number k
of extremes, and number N of simulations.
It is possible to specify either k or sample size as running
parameters.
According to from, to and step, K values of the
parameter range are selected. For these K values N Monte-Carlo
samples are generated. The computed values are written to
a textfile. If running parameters are not wanted, one must select the
corresponding radio button. The result of the simulation is stored as a
trivariate data set with columns containing the running parameters, as
well as the simulated MSE and bias.
Distribution of Estimator (MAX)
Select a df with shape parameter gamma (or likewise, with
shape parameter alpha) by entering its qf in the
edit field on the right-hand side. Use the
predefined function calls provided by the
UserFormula facility and XPL. For example, enter
frechetqf(2,x) to
generate standard Frechet data under the shape parameter alpha=2. In
the edit field below, enter the true parameter value for alpha or
gamma.
Xtremes needs this information to center the data.
Next, select an estimator
on the left-hand side. Then enter values for number n of maxima,
block size m and number of simulations N. Note that the sample size
equals the number of blocks multiplied by the block size. Maxima are
computed for each block. A set of estimates of gamma, say
gamma(k,n,1),..., gamma(k,n,N), is generated and written to a file
of type Xtremes Univariate Data.
Proceed in the same way as described in the POT domain (see also
Distribution of estimator (GP)).
MSE/Bias of Estimator (MAX)
A Monte Carlo Simulation is carried out to estimate the mean squared
error (MSE) and the bias of estimators.
Select a df with shape parameter gamma (or likewise, with
shape parameter alpha) by entering its qf in the
edit field on the right-hand side. Use the
predefined function calls provided by the
UserFormula facility and XPL. For example, enter
frechetqf(2,x) to
generate standard Frechet data under the shape parameter alpha=2. In
the
edit field below, enter the true parameter value for alpha or
gamma.
Xtremes needs this information to calculate MSE and bias.
Next, select an estimator
on the left-hand side and enter values for Number n of
maxima, Block size m and Number N of
simulations. Note that
sample size is the number of maxima multiplied by the block size. Maxima
are computed for each block.
It is possible to specify either n or m as running parameters.
According to from, to and step, K values of the
parameter range are selected. For these K values N Monte-Carlo
samples are generated. The computed values are written to
a textfile. If running parameters are not wanted, one must select the
corresponding radio button. The result of the simulation is stored as a
trivariate data set with columns containing the running parameters, as
well as the simulated MSE and bias.
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