s.gld.from.moments: Get the GLD Parameters from the moments

In ldt: Automated Uncertainty Analysis

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)

ldt documentation built on Sept. 11, 2024, 5:25 p.m.