Hi,

  Some suggestion about the arguments of the function defined below.  Since
theta is calculated with the value of lambda1 and lambda2, there is no need
to include theta in the argument.  Or, your function can be defined as
function(lambda1, lambda2, significance.level)

cover <- function(theta, lambda1, lambda2, significance.level)  { 
  s1 <- rpois(1,lambda1) 
  s2 <- rpois(1,lambda2) 
  theta <- lambda2/(lambda1+lambda2) 
  s <- s1+s2 
  z <- qnorm(1-0.05/2) 
  k <- z^2 
  pi <- s2/s 
  root <- ((s2/s)*(1-s2/s)+k/(4*s))^(1/2) 
  low <- (s2+k/2)/(s+k)-((z*sqrt(s))/(s+k))*root 
  hig <- (s2+k/2)/(s+k)+((z*sqrt(s))/(s+k))*root 
  if (theta >= low & theta <= hig){1} else {0} 
} 



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