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distrHsAT <- function(y2, eta2, sigma2, nu, margin2){
if(margin2 == "probit"){
pdf2 <- dnorm(y2, 0, 1)
p2 <- pnorm(y2, 0, 1)
}
if( margin2 == "logit" ){
p2 <- plogis(y2)
pdf2 <- dlogis(y2)
}
if( margin2 == "cloglog" ){
p2 <- 1-exp(-exp(y2))
pdf2 <- exp(-exp(y2)) * exp(y2)
}
if( margin2 == "cauchit" ){
p2 <- 1 / pi * atan(y2) + 0.5
pdf2 <- 1 / (pi * (1 + y2^2))
}
if(margin2 == "N"){
pdf2 <- dnorm(y2, mean=eta2, sd = sqrt(sigma2))
p2 <- pnorm(y2, mean=eta2, sd = sqrt(sigma2))
}
if(margin2 == "N2"){
# sigma2 which means sigma
pdf2 <- dnorm(y2, mean=eta2, sd = sigma2)
p2 <- pnorm(y2, mean=eta2, sd = sigma2)
}
if(margin2 == "LN"){
pdf2 <- dlnorm(y2, meanlog=eta2, sdlog = sqrt(sigma2))
p2 <- plnorm(y2, meanlog=eta2, sdlog = sqrt(sigma2))
}
if(margin2 == "WEI"){
pdf2 <- sqrt(sigma2)/exp(eta2)*(y2/exp(eta2))^(sqrt(sigma2)-1) * exp(-(y2/exp(eta2))^sqrt(sigma2))
p2 <- 1-exp(-(y2/exp(eta2))^sqrt(sigma2))
}
if(margin2 == "GO"){
pdf2 <- exp(eta2)*exp(sqrt(sigma2)*y2)*exp( ( 1 - exp(sqrt(sigma2)*y2) )*exp(eta2)/sqrt(sigma2) )
p2 <- 1 - exp( ( 1 - exp(sqrt(sigma2)*y2) )*exp(eta2)/sqrt(sigma2) )
}
if(margin2 == "FISK"){
pdf2 <- sqrt(sigma2)*y2^(sqrt(sigma2)-1) / (exp(eta2)^sqrt(sigma2)*(1+(y2/exp(eta2))^sqrt(sigma2))^2)
p2 <- 1/(1+(y2/exp(eta2))^-sqrt(sigma2))
}
if(margin2 == "iG"){
#sigma2 <- ifelse(sigma2 < 0.001, 0.001, sigma2)
pdf2 <- exp(-0.5 * log(2 * pi) - log(sqrt(sigma2)) - (3/2) * log(y2) -
((y2 - exp(eta2))^2)/(2 * sigma2 * (exp(eta2)^2) * y2))
p2 <- pnorm(((y2/exp(eta2)) - 1)/(sqrt(sigma2) * sqrt(y2))) +
exp(2/(exp(eta2)*sigma2))* pnorm(-((y2/exp(eta2)) + 1)/(sqrt(sigma2) * sqrt(y2)))
}
if(margin2 == "LO"){
pdf2 <- dlogis(y2,eta2,sqrt(sigma2)) # exp(-(y2-eta2)/sqrt(sigma2))/(sqrt(sigma2)*(1+exp(-(y2-eta2)/sqrt(sigma2)))^2)
p2 <- plogis(y2,eta2,sqrt(sigma2)) #1/(1+exp(-(y2-eta2)/sqrt(sigma2)))
}
if(margin2 == "rGU"){
pdf2 <- 1/sqrt(sigma2)*exp(-((y2-eta2)/sqrt(sigma2)+exp(-((y2-eta2)/sqrt(sigma2)))))
p2 <- exp(-(exp(-(y2-eta2)/sqrt(sigma2))))
}
if(margin2 == "GU"){
bit <- (exp((y2 - eta2)/sqrt(sigma2)) * (1/sqrt(sigma2)))
bit <- ifelse(bit=="Inf", 1e+290, bit)
pdf2 <- exp(-exp((y2 - eta2)/sqrt(sigma2))) * bit
p2 <- 1 - exp(-exp((y2 - eta2)/sqrt(sigma2)))
}
if(margin2 %in% c("GA")){
sigma2 <- ifelse(sigma2 < 0.006, 0.006, sigma2) # related to gamma function
pdf2 <- dgamma(y2, shape = 1/sigma2, scale = exp(eta2) * sigma2)
p2 <- pgamma(y2, shape = 1/sigma2, scale = exp(eta2) * sigma2)
}
if(margin2 %in% c("GA2")){
sigma2 <- ifelse(sigma2 < 0.006, 0.006, sigma2) # related to gamma function
pdf2 <- exp(eta2)^(sqrt(sigma2)) * y2^(sqrt(sigma2) -1) * exp(-(y2*exp(eta2))) / gamma(sqrt(sigma2))
p2 <- pgamma(y2, shape = sqrt(sigma2), rate= exp(eta2))
}
if(margin2 %in% c("GGA")){
pdf2 <- (sqrt(sigma2) / gamma(nu))*(y2^(sqrt(sigma2)*nu -1) / exp(eta2)^(sqrt(sigma2)*nu))* exp(-(y2/exp(eta2))^sqrt(sigma2))
p2 <- pgamma(exp((log(y2) - log(exp(eta2))) * sqrt(sigma2)), shape = 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)
pdf2 <- dgamma(y2, shape = 1/sigma2, scale = eta2 * sigma2)
p2 <- pgamma(y2, shape = 1/sigma2, scale = eta2 * sigma2)
}
if(margin2 == "DAGUM"){
pdf2 <- sqrt(sigma2)*nu/y2*( ((y2/exp(eta2))^(sqrt(sigma2)*nu)) / ( (y2/exp(eta2))^sqrt(sigma2) + 1 )^(nu+1) )
p2 <- ( 1 + (y2/exp(eta2))^-sqrt(sigma2) )^-nu
}
if(margin2 == "SM"){
pdf2 <- sqrt(sigma2)*nu*y2^(sqrt(sigma2)-1)*(exp(eta2)^sqrt(sigma2)*(1+(y2/exp(eta2))^sqrt(sigma2))^(nu+1) )^-1
p2 <- 1 - (1+(y2/exp(eta2))^sqrt(sigma2))^-nu
}
if(margin2 == "BE"){
pdf2 <- dbeta(y2, shape1 = plogis(eta2) * (1 - sigma2)/(sigma2), shape2 = (1-plogis(eta2))*(1 - sigma2)/(sigma2))
p2 <- pbeta(y2, shape1 = plogis(eta2) * (1 - sigma2)/(sigma2), shape2 = (1-plogis(eta2))*(1 - sigma2)/(sigma2))
}
p2 <- mm(p2)
epsilon <- 0.0000001
pdf2 <- ifelse(pdf2 < epsilon, epsilon, pdf2 )
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
}
# for safety
pdf2 = ifef(pdf2)
p2 = ifef(p2)
list(pdf2 = pdf2, p2 = p2)
}
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