# Generalised Gamma denisty from Stacy (1962)
dStacy_gamma <- function(x, mu, alpha, phi) {
alpha <- abs(alpha)
alpha/gamma(phi)*mu^{alpha*phi}*x^{alpha*phi - 1}*exp(-(mu*x)^{alpha})
}
# gb2 density
dgb2 <- function(x,shape1,scale,shape2,shape3){
y <- (x/scale)^shape1
dy_dx <- (shape1/scale)*(x/scale)^(shape1-1)
z <- y/(1+y)
z[z==1] <- 1-.Machine$double.eps
dz_dy <- (1+y)^(-2)
dens <- dbeta(z, shape2, shape3) * dz_dy * dy_dx
v <- (x==Inf)
dens[v] <- 0
return(dens)
}
pgb2 <- function(x,shape1,scale,shape2,shape3){
y <- (x/scale)^shape1
z <- y/(1+y)
prob <- pbeta(z, shape2, shape3)
v <- (x==Inf)
prob[v] <- 1
return(prob)
}
# Lomax density
dLomax <- function(x, scale, shape) {
return((shape/scale)*(1+(x/scale))^{-(shape+1)})
}
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