JProfileMLE.phitheta <- function(x, y, mu0, sx, sy){
#### jointly obtain the MLE of phi and theta
log.lik <- function(para, yy, xx, mmu, sx, sy){
s = para[1]
t = para[2]
loglik = sum(dnbinom(yy, size = mmu*(s^{-1} - 1),
prob = 1/(1+sy*t), log = TRUE) +
dnbinom(xx, size = (1 - mmu)*(s^{-1} - 1),
prob = 1/(1+sx*t), log = TRUE)
)
loglik
}
res = optim(c(exp(-5), exp(1)),
log.lik,
yy = y, xx = x,
mmu = mu0, sx = sx, sy = sy,
method = "L-BFGS-B",
lower = rep(0.00001, 2),
upper = c(0.999, exp(700)),
control = list(fnscale = -1),
hessian = FALSE)
return(res)
}
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