Nothing
"lmompe3" <-
function(para) {
z <- list(L1 = NULL,
L2 = NULL,
TAU3 = NULL,
TAU4 = NULL,
TAU5 = NULL,
LCV = NULL,
L3 = NULL,
L4 = NULL,
L5 = NULL,
source = "lmompe3"
)
if(! are.parpe3.valid(para)) return()
attributes(para$para) <- NULL
# SMALL IS USED TO TEST WHETHER SKEWNESS IS EFFECTIVELY ZERO
SMALL <- 1e-6
# CONST IS 1/SQRT(PI)
CONST <- 1/sqrt(pi)
# COEFFICIENTS OF RATIONAL-FUNCTION APPROXIMATIONS
# A0 IS 1/SQRT(3*PI)
# C0 IS TAU-4 FOR THE NORMAL DISTRIBUTION
A0 <- 1/sqrt(3*pi)
A1 <- 0.16869150
A2 <- 0.78327243e-1
A3 <- -0.29120539e-2
B1 <- 0.46697102
B2 <- 0.24255406
C0 <- 0.12260172
C1 <- 0.53730130e-1
C2 <- 0.43384378e-1
C3 <- 0.11101277e-1
D1 <- 0.18324466
D2 <- 0.20166036
E1 <- 0.23807576e1
E2 <- 0.15931792e1
E3 <- 0.11618371
F1 <- 0.51533299e1
F2 <- 0.71425260e1
F3 <- 0.19745056e1
G1 <- 0.21235833e1
G2 <- 0.41670213e1
G3 <- 0.31925299e1
H1 <- 0.90551443e1
H2 <- 0.26649995e2
H3 <- 0.26193668e2
SIGMA <- para$para[2]
# LAMBDA-1
z$L1 <- para$para[1]
# LAMBDA-2
GAMMA <- para$para[3]
if(abs(GAMMA) < SMALL) {
# CASE OF ZERO SKEWNESS
z$L2 <- CONST*SIGMA
z$TAU3 <- 0
z$TAU4 <- C0
z$L3 <- z$L2*z$TAU3
z$L4 <- z$L2*z$TAU4
# NO TAU5 AVAILABLE
}
else {
ALPHA <- 4/(GAMMA*GAMMA)
BETA <- abs(0.5*SIGMA*GAMMA)
ALAM2 <- CONST*exp(lgamma(ALPHA+0.5)-lgamma(ALPHA))
z$L2 <- ALAM2*BETA
# HIGHER MOMENTS
if(ALPHA < 1) {
Z <- ALPHA
z$TAU3 <- (((E3*Z+E2)*Z+E1)*Z+1)/(((F3*Z+F2)*Z+F1)*Z+1)
if(GAMMA < 0) z$TAU3 <- -z$TAU3
z$TAU4 <- (((G3*Z+G2)*Z+G1)*Z+1)/(((H3*Z+H2)*Z+H1)*Z+1)
z$L3 <- z$L2*z$TAU3
z$L4 <- z$L2*z$TAU4
}
else {
Z <- 1/ALPHA
z$TAU3 <- sqrt(Z)*(((A3*Z+A2)*Z+A1)*Z+A0)/((B2*Z+B1)*Z+1)
if(GAMMA < 0) z$TAU3 <- -z$TAU3
z$TAU4 <- (((C3*Z+C2)*Z+C1)*Z+C0)/((D2*Z+D1)*Z+1)
z$L3 <- z$L2*z$TAU3
z$L4 <- z$L2*z$TAU4
}
}
z$LCV <- z$L2/z$L1
z <- lmorph(z)
return(z)
}
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