Nothing
distrHsAT1 <- function(y2.st, eta2, sigma2, nu, margin2){
if(margin2 %in% c("N")){
y2 <- y2.st
mu2 <- eta2
der2p2.dery22 <- -(1/sqrt(2 * pi * sigma2) * (exp(-0.5 * (y2 - mu2)^2/sigma2) * (0.5 * (2 * (y2 - mu2))/sigma2)))
dery.dery.st <- 1
der2y.dery.st2 <- 0
}
if(margin2 %in% c("LN")){
y2 <- dery.dery.st <- der2y.dery.st2 <- exp(y2.st)
mu2 <- exp(eta2)
der2p2.dery22 <- -(1/(y2 * sqrt(sigma2) * sqrt(2 * pi)) * (exp(-0.5 * (log(y2) - mu2)^2/sigma2) * (0.5 * (2 * (1/y2 * (log(y2) - mu2)))/sigma2)) +
sqrt(sigma2) * sqrt(2 * pi)/(y2 * sqrt(sigma2) * sqrt(2 * pi))^2 * exp(-0.5 * (log(y2) - mu2)^2/sigma2))#D(expression(1/(y2*sqrt(sigma2)*sqrt(2*pi))*exp(-0.5*(log(y2)-mu2)^2/sigma2)),"y2")
}
###################
if(margin2 == "DAGUM"){
y2 <- dery.dery.st <- der2y.dery.st2 <- exp(y2.st)
mu2 <- exp(eta2)
der2p2.dery22 <- sqrt(sigma2) * nu/y2 * ((y2/mu2)^((sqrt(sigma2) * nu) - 1) *
((sqrt(sigma2) * nu) * (1/mu2))/((y2/mu2)^sqrt(sigma2) +
1)^(nu + 1) - ((y2/mu2)^(sqrt(sigma2) * nu)) * (((y2/mu2)^sqrt(sigma2) +
1)^((nu + 1) - 1) * ((nu + 1) * ((y2/mu2)^(sqrt(sigma2) -
1) * (sqrt(sigma2) * (1/mu2)))))/(((y2/mu2)^sqrt(sigma2) +
1)^(nu + 1))^2) - sqrt(sigma2) * nu/y2^2 * (((y2/mu2)^(sqrt(sigma2) *
nu))/((y2/mu2)^sqrt(sigma2) + 1)^(nu + 1))
}
####
if(margin2 == "SM"){
y2 <- dery.dery.st <- der2y.dery.st2 <- exp(y2.st)
mu2 <- exp(eta2)
der2p2.dery22 <- sqrt(sigma2) * nu * (y2^((sqrt(sigma2) - 1) - 1) * (sqrt(sigma2) -
1)) * (mu2^sqrt(sigma2) * (1 + (y2/mu2)^sqrt(sigma2))^(nu +
1))^-1 - sqrt(sigma2) * nu * y2^(sqrt(sigma2) - 1) * ((mu2^sqrt(sigma2) *
(1 + (y2/mu2)^sqrt(sigma2))^(nu + 1))^-(1 + 1) * (mu2^sqrt(sigma2) *
((1 + (y2/mu2)^sqrt(sigma2))^((nu + 1) - 1) * ((nu + 1) *
((y2/mu2)^(sqrt(sigma2) - 1) * (sqrt(sigma2) * (1/mu2)))))))
}
###
if(margin2 == "FISK"){
y2 <- dery.dery.st <- der2y.dery.st2 <- exp(y2.st)
mu2 <- exp(eta2)
der2p2.dery22 <- sqrt(sigma2) * (y2^((sqrt(sigma2) - 1) - 1) * (sqrt(sigma2) -
1))/(mu2^sqrt(sigma2) * (1 + (y2/mu2)^sqrt(sigma2))^2) -
sqrt(sigma2) * y2^(sqrt(sigma2) - 1) * (mu2^sqrt(sigma2) *
(2 * ((y2/mu2)^(sqrt(sigma2) - 1) * (sqrt(sigma2) * (1/mu2)) *
(1 + (y2/mu2)^sqrt(sigma2)))))/(mu2^sqrt(sigma2) *
(1 + (y2/mu2)^sqrt(sigma2))^2)^2
}
####
if(margin2 == "WEI"){
y2 <- dery.dery.st <- der2y.dery.st2 <- exp(y2.st)
mu2 <- exp(eta2)
der2p2.dery22 <- sqrt(sigma2)/mu2 * ((y2/mu2)^((sqrt(sigma2) - 1) - 1) * ((sqrt(sigma2) -
1) * (1/mu2))) * exp(-(y2/mu2)^sqrt(sigma2)) - sqrt(sigma2)/mu2 *
(y2/mu2)^(sqrt(sigma2) - 1) * (exp(-(y2/mu2)^sqrt(sigma2)) *
((y2/mu2)^(sqrt(sigma2) - 1) * (sqrt(sigma2) * (1/mu2))))
}
if(margin2 == "GO"){
y2 <- dery.dery.st <- der2y.dery.st2 <- exp(y2.st)
mu2 <- exp(eta2)
der2p2.dery22 <- mu2 * exp(mu2 * (1 - exp(y2 * sqrt(sigma2)))/sqrt(sigma2)) *
exp(y2 * sqrt(sigma2)) * (sigma2/sqrt(sigma2) - mu2 * exp(y2 *
sqrt(sigma2)))
}
if(margin2 == "BE"){
#########################
y2 <- plogis(y2.st)
mu2 <- plogis(eta2)
a <- mu2 * (1 - sigma2)/(sigma2)
b <- a * (1 - mu2)/mu2
derp2.dery2 <- dbeta(y2, shape1 = mu2 * (1 - sigma2)/(sigma2), shape2 = (1-mu2)*(1 - sigma2)/(sigma2))
der2p2.dery22 <- derp2.dery2 * ( (a + b - 2) * y2 - (a - 1) ) / ( ( y2 - 1 ) * y2 ) # from wikipedia
dery.dery.st <- (1 - exp(y2.st)/(1 + exp(y2.st))) * exp(y2.st)/(1 + exp(y2.st))
der2y.dery.st2 <- (1 - (3 - 2 * (exp(y2.st)/(1 + exp(y2.st)))) * exp(y2.st)/(1 + exp(y2.st))) * exp(y2.st)/(1 + exp(y2.st))
}
####
if(margin2 == "iG"){
y2 <- dery.dery.st <- der2y.dery.st2 <- exp(y2.st)
mu2 <- exp(eta2)
der2p2.dery22 <- -(exp(-0.5 * log(2 * pi) - log(sqrt(sigma2)) - (3/2) * log(y2) -
((y2 - mu2)^2)/(2 * sigma2 * (mu2^2) * y2)) * ((3/2) * (1/y2) +
(2 * (y2 - mu2)/(2 * sigma2 * (mu2^2) * y2) - ((y2 - mu2)^2) *
(2 * sigma2 * (mu2^2))/(2 * sigma2 * (mu2^2) * y2)^2)))
}
####
if(margin2 == "LO"){
y2 <- y2.st
mu2 <- eta2
der2p2.dery22 <- exp((y2 - mu2)/sqrt(sigma2)) * (1/sqrt(sigma2))/(sqrt(sigma2) *
(1 + exp((y2 - mu2)/sqrt(sigma2)))^2) - exp((y2 - mu2)/sqrt(sigma2)) *
(sqrt(sigma2) * (2 * (exp((y2 - mu2)/sqrt(sigma2)) * (1/sqrt(sigma2)) *
(1 + exp((y2 - mu2)/sqrt(sigma2))))))/(sqrt(sigma2) *
(1 + exp((y2 - mu2)/sqrt(sigma2)))^2)^2
dery.dery.st <- 1
der2y.dery.st2 <- 0
}
##########################
if(margin2 == "rGU"){
y2 <- y2.st
mu2 <- eta2
der2p2.dery22 <- -(1/sqrt(sigma2) * (exp(-((y2 - mu2)/sqrt(sigma2) + exp(-((y2 -
mu2)/sqrt(sigma2))))) * (1/sqrt(sigma2) - exp(-((y2 - mu2)/sqrt(sigma2))) *
(1/sqrt(sigma2)))))
dery.dery.st <- 1
der2y.dery.st2 <- 0
}
######################################
if(margin2 == "GU"){
y2 <- y2.st
mu2 <- eta2
der2p2.dery22 <- exp(-exp((y2 - mu2)/sqrt(sigma2))) * (exp((y2 - mu2)/sqrt(sigma2)) *
(1/sqrt(sigma2)) * (1/sqrt(sigma2))) - exp(-exp((y2 - mu2)/sqrt(sigma2))) *
(exp((y2 - mu2)/sqrt(sigma2)) * (1/sqrt(sigma2))) * (exp((y2 -
mu2)/sqrt(sigma2)) * (1/sqrt(sigma2)))
dery.dery.st <- 1
der2y.dery.st2 <- 0
}
if(margin2 == "GA"){
sigma2 <- ifelse(sigma2 < 0.006, 0.006, sigma2)
y2 <- dery.dery.st <- der2y.dery.st2 <- exp(y2.st)
mu2 <- exp(eta2)
der2p2.dery22 <- (y2^((1/sigma2 - 1) - 1) * (1/sigma2 - 1) * exp(-y2/(mu2 *
sigma2)) - y2^(1/sigma2 - 1) * (exp(-y2/(mu2 * sigma2)) *
(1/(mu2 * sigma2))))/(gamma(1/sigma2)*(mu2 * sigma2))^(1/sigma2)
}
if(margin2 == "GA2"){
sigma2 <- ifelse(sigma2 < 0.006, 0.006, sigma2)
y2 <- dery.dery.st <- der2y.dery.st2 <- exp(y2.st)
mu2 <- exp(eta2)
der2p2.dery22 <- exp(-(mu2 * y2)) * (mu2^sqrt(sigma2) * y2^(sqrt(sigma2) - 2) *
(sqrt(sigma2) - 1) - mu2^(1 + sqrt(sigma2)) * y2^(sqrt(sigma2) -
1))/gamma(sqrt(sigma2))
}
if(margin2 == "GGA"){
y2 <- dery.dery.st <- der2y.dery.st2 <- exp(y2.st)
mu2 <- exp(eta2)
der2p2.dery22 <- exp(-(y2/mu2)^sqrt(sigma2)) * (y2^(nu * sqrt(sigma2) - 2) * (nu *
sqrt(sigma2) - 1) * sqrt(sigma2)/mu2^(nu * sqrt(sigma2)) -
sigma2 * y2^(nu * sqrt(sigma2) - 1) * (y2/mu2)^(sqrt(sigma2) -
1)/mu2^(1 + nu * sqrt(sigma2)))/gamma(nu)
}
if(margin2 %in% c("GAi")){
sigma2 <- ifelse(sigma2 < 0.006, 0.006, sigma2) # related to gamma function
eta2 <- ifelse(eta2 < 0.0000001, 0.0000001, eta2)
y2 <- dery.dery.st <- der2y.dery.st2 <- exp(y2.st)
mu2 <- eta2
der2p2.dery22 <- (y2^((1/sigma2 - 1) - 1) * (1/sigma2 - 1) * exp(-y2/(mu2 * sigma2)) -
y2^(1/sigma2 - 1) * (exp(-y2/(mu2 * sigma2)) * (1/(mu2 *
sigma2))))/ (gamma(1/sigma2)*(mu2 * sigma2))^(1/sigma2)
}
ifef <- function(dv){
epsilon <- 0.0000001
dv <- ifelse(is.na(dv), epsilon, dv )
dv <- ifelse(dv == Inf , 8.218407e+20, dv )
dv <- ifelse(dv == -Inf , -8.218407e+20, dv )
dv
}
der2p2.dery22 <- ifef(der2p2.dery22 )
dery.dery.st <- ifef(dery.dery.st )
der2y.dery.st2 <- ifef(der2y.dery.st2)
list(der2p2.dery22 = der2p2.dery22, dery.dery.st = dery.dery.st, der2y.dery.st2 = der2y.dery.st2)
}
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