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Testing Menu
Univariate Mode
Discrete domain: Poisson, Goodness-of-Fit SUM domain: Gaussian MAX domain: LR(EV0/EV) POT domain: LR(GP0/GP) Hasofer-Wang(GP0/GP)
Multivariate Mode*
SUM domain: Gaussian* Wilcoxon*
Recall that the Poisson model is rejected for small p-values.
one-sided:
H0: mu < mu0 against H1: mu > mu0,
two-sided*:
H0: mu = mu0 against H1: mu <> mu0,
with
In the dialog box, specify
Press OK to obtain the p-value. Recall that for small p-values
the null hypothesis H0 is rejected (Statistical Analysis, Section
3.3).
The significance level is attained with a higher accuracy by
employing a Bartlett correction; in this case a modified p-value
is used.
Recall that the Gumbel model is rejected for small p-values.
Choose the number of upper extremes on which the test should
be based on. Alternatively, if exceedances over a threshold u are
dealt with, prepare the data set in the data editor: Take the
exceedances over u and include u in the data set. Then apply
the LR option with number of extremes equal to the full
sample size (which is the default value).
The significance level is attained with a higher accuracy by
employing a Bartlett correction; in this case a modified p-value
is used.
The output consists again of the p-value. The
hypothesis of an exponential-like upper tail is rejected for
small p-values.
The output consists again of
the p-value. Recall that the hypothesis of an
exponential-like upper tail must be rejected for small p-values.
Let mux, sigmax and muy, sigmay denote the
means and standard deviations of the Gaussian distributions
in the 1st and 2nd component. Within the Gaussian model one
is testing
one-sided:
H0: mux <= muy against H1: mux > muy,
two-sided:
H0: mux = muy against H1: mux <> muy,
with
In the dialog box, specify
Press OK to obtain the p-value. Recall that for small p-values
the null hypothesis H0 is rejected (Statistical Analysis, Section
3.3).
Poisson, Goodness-of-Fit
The Poisson model can be tested by means of
chi-square- and likelihood-ratio-tests (see
Statistical Analysis, pages 106-107). First, fix cell
boundaries in the left-hand edit field.
Equally sized cells can be obtained by means of
the From, To and Step-Width options.
Pressing OK, the pertaining frequencies
within the cells (in the right-hand field) and the p-value
are displayed.Gaussian testing, one-sample
Let mu denote the mean and sigma the
standard deviation of a Gaussian distribution.
Within the Gaussian model one is testing
LR(EV0/EV)
Within the EV model, the null hypothesis gamma = 0 is tested against
the alternative gamma <> 0 with unknown location and scale
parameters by means of a Likelihood-Ratio-Test. Thus,
the Gumbel distributions are tested against other EV
distributions. The output consists again of the p-value.LR(GP0/GP)
Within the GP model, the null hypothesis gamma = 0 is tested against
the alternative gamma <> 0 with unknown scale
parameters by means of a likelihood-ratio-test. More precisely,
exponential-like upper tails are tested against other
GP-like upper tails (see Statistical Analysis, page 154).Hasofer-Wang(GP0/GP)
This is another test besides the likelihood-ratio-test
(see LR(GP0/GP) ) for
testing exponential-like upper tails against other GP-like
upper tails. The Hashofer-Wang test is
based on the reciprocal squared coefficient of variation
(see Statistical Analysis, page 154). Make sure that the
shape parameter gamma is smaller than 1/2.Gaussian testing, two-sample*
The test procedures are applied to bivariate data of type
Xtremes Multivariate Data. The
data x[1], ... , x[n] and y[1], ... , y[m] in
the 1st and 2nd column may be of a different length whereby
empty entries are filled with a full stop. Notice that two
univariate data sets may be combined to a bivariate one by
using the Data... Convert to... Multivariate Data... option.
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