Nothing
pdfP3 = function(xp3, alpha, beta, tau){
expon = ifelse((((xp3 - tau)/beta) < 0) & (((alpha - 1) %% 1) != 0), round(alpha - 1), alpha - 1)
density = (1/(abs(beta) * gamma(alpha))) * ((xp3 - tau)/beta)^expon * exp(-(xp3 - tau)/beta)
return(density)
}
###########################################################
#' @importFrom stats pnorm pgamma
cdfP3 = function(xp3, mu_p = x_bar, sigma_p = s_x, gamma_p = C_s){
if(xp3 <= 0){PP3 = 0; return(PP3)}
if(sigma_p <= 0){stop('invalid parameters')}
if(gamma_p <= 1e-06){PP3 = pnorm(xp3, mu_p, sigma_p); return(PP3)}else{
alpha = 4/gamma_p^2
z = 2 * (xp3 - mu_p)/(sigma_p * gamma_p) + alpha
PP3 = pgamma(pmax(0, z), alpha)
if(gamma_p < 0){PP3 = 1 - PP3}
return(PP3)
}
}
###########################################################
P3P = function(xp3, P){cdfP3(xp3) - P}
###########################################################
#' @importFrom stats qnorm qgamma
quaP3 = function(P, mu_p = x_bar, sigma_p = s_x, gamma_p = C_s){
if(P < 0){stop('invalid probability')}
if(sigma_p <= 0){stop('invalid parameters')}
if(abs(gamma_p) <= 1e-08){QP3 = qnorm(P, mu_p, sigma_p); return(QP3)}else{
alpha = 4/gamma_p^2
beta = abs(0.5 * sigma_p * gamma_p)
QP3 = ifelse(gamma_p > 0, mu_p - alpha * beta + beta * pmax(0, qgamma(P, alpha)),
mu_p + alpha * beta - beta * pmax(0, qgamma(1 - P, alpha)))
return(QP3)}
}
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