#' lnb
#'
#' \code{lnb} returns the log likelihood f(x),
#' where x ~ Nb(alpha, beta/(E+beta) )
#'
#' @export
#' @param x a scalar. A realization from negative binomial distribution.
#' @param alpha shape parameter in gamma distribution
#' @param beta rate parameter in gamma distribution
#' @param E a scalar. Normalizing constant for the observed chain x.
#' @return Log likelihood f(x)
#'
#' @examples
#' x <- 50
#' alpha <- 1
#' beta <- 0.1
#' E <- 10
#' lnb(x, alpha, beta, E)
lnb <- function(x, alpha, beta, E){
p <- beta/(E+beta)
lf <- dnbinom(x, alpha, p, log=TRUE)
return(lf)
}
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