estimkiener11 {FatTailsR} | R Documentation |
Estimation Functions with 5, 7 or 11 Quantiles
Description
Several functions to estimate the parameters of asymmetric Kiener distributions with just 5, 7 or 11 quantiles.
Usage
estimkiener11(x11, p11, ord = 7, maxk = 10)
estimkiener7(x7, p7, maxk = 10)
estimkiener5(x5, p5, maxk = 20, maxe = 0.9)
Arguments
ord |
integer. Option for probability selection and treatment. |
maxk |
numeric. Maximum value for k (kappa). |
x5 , x7 , x11 |
vector of 5, 7 or 11 quantiles. |
p5 , p7 , p11 |
vector of 5, 7 or 11 probabilities. |
maxe |
numeric. Maximum value for abs(e) (epsilon).
Maximum is |
Details
These functions, called by paramkienerX5
, paramkienerX7
,
paramkienerX
, use 5, 7 or 11 probabilites and quantiles
to estimate the parameters of Kiener distributions.
p5, x5
are obtained with functions fiveprobs(X)
and quantile(p5)
.
p7, x7
are obtained with functions sevenprobs(X)
and quantile(p7)
.
p11, x11
are obtained with functions elevenprobs(X)
and quantile(p11)
.
The extraction of the 11 probabilities is controlled with the option ord
which can take 12 integer values, ord = 7
being the default.
Small dataset should consider ord = 5
and
large dataset can consider ord = 12
:
-
c(p1, 0.35, 0.50, 0.65, 1-p1)
-
c(p2, 0.35, 0.50, 0.65, 1-p2)
-
c(p1, p2, 0.35, 0.50, 0.65, 1-p2, 1-p1)
-
c(p1, p2, p3, 0.35, 0.50, 0.65, 1-p3, 1-p2, 1-p1)
-
c(p1, 0.25, 0.50, 0.75, 1-p1)
-
c(p2, 0.25, 0.50, 0.75, 1-p2)
-
c(p1, p2, 0.25, 0.50, 0.75, 1-p2, 1-p1)
-
c(p1, p2, p3, 0.25, 0.50, 0.75, 1-p3, 1-p2, 1-p1)
-
c(p1, 0.25, 0.35, 0.50, 0.65, 0.75, 1-p1)
-
c(p2, 0.25, 0.35, 0.50, 0.65, 0.75, 1-p2)
-
c(p1, p2, 0.25, 0.35, 0.50, 0.65, 0.75, 1-p2, 1-p1)
-
c(p1, p2, p3, 0.25, 0.35, 0.50, 0.65, 0.75, 1-p3, 1-p2, 1-p1)
p5 = fiveprobs(X)
corresponds to c(p1, 0.25, 0.50, 0.75, 1-p1)
.
p7 = sevenprobs(X)
corresponds to c(p1, p2, 0.25, 0.50, 0.75, 1-p2, 1-p1)
.
The above probabilities are then transfered to the quantile
function
whose parameter type
can change significantly the extracted quantiles.
Our experience is that type = 6
is appropriate when k > 1.9
and
type = 5
is appropriate when k < 1.9
.
Other types type = 8
and type = 9
can be considered as well.
The other types should be ignored.
(Note: when k < 1.5
, algorithm algo = "reg"
returns better
results).
Parameter maxk controls the maximum allowed value for estimated parameter k.
Reasonnable values are maxk = 10, 15, 20
. Default is maxk = 10
to be consistent with regkienerLX
.
See Also
elevenprobs
, paramkienerX
, quantile
,
roundcoefk
.
Examples
require(timeSeries)
## Choose j in 1:16. Choose ord in 1:12 (7 is default)
j <- 5
ord <- 5
DS <- getDSdata()
p11 <- elevenprobs(DS[[j]])
x11 <- quantile(DS[[j]], probs = p11, na.rm = TRUE, names = TRUE, type = 6)
round(estimkiener11(x11, p11, ord), 3)
## Compare the results obtained with the 12 different values of ord on stock j
compare <- function(ord, x11, p11) {estimkiener11(x11, p11, ord)}
coefk <- t(sapply(1:12, compare, x11, p11))
rownames(coefk) <- 1:12
mcoefk <- apply(coefk, 2, mean) # the mean of the 12 results above
roundcoefk(rbind(coefk, mcoefk), 13)