View source: R/sample-rextmo.R
rextmo | R Documentation |
Draws n
iid samples from a d
-variate extendible Marshall–Olkin
distribution parametrized by a Bernstein function bf
.
rextmo(n, d, bf, method = c("MDCM", "AM", "ESM"))
n |
An integer for the number of samples. |
d |
An integer for the dimension. |
bf |
A BernsteinFunction representing the Bernstein function of a extendible Marshall–Olkin distribution. |
method |
A string indicating which sampling algorithm should be used.
Use |
The extendible Marshall–Olkin distribution has the survival function
\bar{F}{(t)}
= \exp{\left\{
- \sum_{i=1}^{d}{ {[ \psi{(i)} - \psi{(i-1)} ]} t_{[i]} }
\right\}} ,
\quad t = {(t_{1}, \ldots, t_{d})} > 0 ,
for Bernstein functions \psi
, see BernsteinFunction, and
t_{[1]} \geq \cdots \geq t_{[d]}
, see \insertCiteMai2017armo.
The relationship between Bernstein functions and
exchangeable shock-size arrival intensities of the
exchangeable Marshall–Olkin distribution, see rexmo()
, is as follows:
\eta_{i}
= \binom{d}{i} {(-1)}^{i-1} \Delta{ \psi{(d-i)} } ,
\quad i \in {\{ 1 , \ldots , d \}} .
This formula for the exchangeable shock-size arrival intensities is not
numerically stable in higher dimensions, and rextmo()
uses
approximation techniques from \insertCiteSloot2022armo to calculate them.
rextmo
returns a numeric matrix of size n
x d
rows and d
. Each row
corresponds to an independently and identically (iid) distributed sample from
a d
-variate extendible Marshall–Olkin distribution with specified
parameters.
Other sampling-algorithms:
rexmo()
,
rmo()
,
rpextmo()
rextmo(
10, 3,
AlphaStableBernsteinFunction(alpha = log2(2 - 0.5))
)
# independence
rextmo(
10, 3,
LinearBernsteinFunction(scale = 1)
)
# comonotone
rextmo(
10, 3,
ConstantBernsteinFunction(constant = 1)
)
rextmo(
10, 3,
AlphaStableBernsteinFunction(alpha = log2(2 - 0.5)),
method = "AM"
)
# independence
rextmo(
10, 3,
LinearBernsteinFunction(scale = 1),
method = "AM"
)
# comonotone
rextmo(
10, 3,
ConstantBernsteinFunction(constant = 1),
method = "AM"
)
rextmo(
10, 3,
AlphaStableBernsteinFunction(alpha = log2(2 - 0.5)),
method = "ESM"
)
# independence
rextmo(
10, 3,
LinearBernsteinFunction(scale = 1),
method = "ESM"
)
# comonotone
rextmo(
10, 3,
ConstantBernsteinFunction(constant = 1),
method = "ESM"
)
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