| s.gld.from.moments {ldt} | R Documentation |
Get the GLD Parameters from the moments
Description
Calculates the parameters of the generalized lambda distribution (FKML), given the first four moments of the distribution.
Usage
s.gld.from.moments(
mean = 0,
variance = 1,
skewness = 0,
excessKurtosis = 0,
type = 0,
start = NULL,
nelderMeadOptions = get.options.neldermead()
)
Arguments
mean |
A number for the mean of the distribution. |
variance |
A number for the variance of the distribution. |
skewness |
A number for the skewness of the distribution. |
excessKurtosis |
A number for the excess kurtosis of the distribution. |
type |
An integer to restrict the shape of the distribution. See details section. |
start |
A numeric vector of size 2 for the starting value. |
nelderMeadOptions |
A list of options for Nelder-Mead algorithm. Use get.options.neldermead for initialization. |
Details
The type of the distribution is determined by one or two restrictions:
-
type 0: general, no restriction
-
type 1: symmetric 'type 0', p3 == p4
-
type 2: uni-modal continuous tail, p3 < 1 & p4 < 1
-
type 3: symmetric 'type 2', p3 == p4
-
type 4: uni-modal continuous tail finite slope, p3 <= 0.5 & p4 <= 0.5
-
type 5: symmetric 'type 4', p3 == p4
-
type 6: uni-modal truncated density curves, p3 >= 2 & p4 >= 2 (includes uniform distribution)
-
type 7: symmetric 'type 6', p3 == p4
-
type 8: S shaped, (p3 > 2 & 1 < p4 < 2) or (1 < p3 < 2 & p4 > 2)
-
type 9: U shaped, (1 < p3 <= 2) and (1 < p4 <= 2)
-
type 10: symmetric 'type 9', p3 == p4
-
type 11: monotone, p3 > 1 & p4 <= 1
Value
A vector of length 5. The first 4 elements are the parameters of the GLD distribution. The last one is the number of iterations.
Examples
res <- s.gld.from.moments(0,1,0,0, start = c(0,0), type = 4)
probs <- seq(0.1,0.9,0.1)
x <- s.gld.quantile(probs, res[1],res[2],res[3],res[4])
y <- s.gld.density.quantile(probs, res[1],res[2],res[3],res[4])
plot(x,y)
lines(x,y)