LRGumbel.test {Renext} | R Documentation |
Likelihood Ratio test for the Gumbel distribution
Description
Likelihood Ratio test of Gumbel vs. GEV
Usage
LRGumbel.test(x,
alternative = c("frechet", "GEV"),
method = c("num", "sim", "asymp"),
nSamp = 1500,
simW = FALSE)
Arguments
x |
Numeric vector of sample values. |
alternative |
Character string describing the alternative distribution. |
method |
Method used to compute the |
nSamp |
Number of samples for a simulation, if |
simW |
Logical. If this is set to |
Details
The asymptotic distribution of the Likelihood-ratio statistic is
known. For the GEV alternative, this is a chi-square distribution with
one df. For the Fréchet alternative, this is the distribution of a
product XY
where X
and Y
are two independent random
variables following a Bernoulli distribution with probability
parameter p = 0.5
and a chi-square distribution with one df.
When
method
is"num"
, a numerical approximation of the distribution is used.When
method
is"sim"
,nSamp
samples of the Gumbel distribution with the same size asx
are drawn and the LR statistic is computed for each sample. Thep
-value is simply the estimated probability that a simulated LR is greater than the observed LR. This method requires more computation time than the tow others.Finally when
method
is"asymp"
, the asymptotic distribution is used.
Value
A list of results with elements statistic
, p.value
and method
. Other elements are
alternative |
Character describing the alternative hypothesis. |
W |
If |
Note
For the Fréchet alternative, the distribution of the test statistic
has mixed type: it can take any positive value as well as the
value 0
with a positive probability mass. The probability mass
is the probability that the ML estimate of the GEV shape parameter is
negative.
When method
is "sim"
, the computation can be slow
because each of the nSamp
simulated values requires two
optimisations. The "asymp"
method provides an acceptable
precision for n \geq 50
, and may even be used for
n \geq 30
.
Author(s)
Yves Deville
Examples
set.seed(1234)
x <- rgumbel(60)
res <- LRGumbel.test(x)