R/mle_zibell.r

In countDM: Estimation of Count Data Models

#' @export
#' @import maxLik
#' @import stats
#' @import numbers
#' @importFrom miscTools stdEr

mle_zibell <- function(x, alpha, lambda) {

  n<- length(x)
  S0 <- sum( x == 0)
  x1 <- x[x > 0]
  x1
  S <- sum(x1)

  com <- (n - S0)

  loglik<-function(p){
    alpha <- p[1]
    lambda <- p[2]
    loglik <- S0*log(p[1]+(1-p[1])*exp((1-exp(p[2]))))+com*log(1-p[1])+com*(1-exp(p[2]))+S*log(p[2])-sum( lgamma(x1 + 1) )+sum(log(sapply(x1,bell)))

  }
  res <- suppressWarnings(maxLik(loglik,start=c(alpha,lambda)))
  aux <- cbind(coef(res), miscTools::stdEr(res))
  colnames(aux) = c("MLE", "SE")

  aux1 = cbind(AIC(res))
  colnames(aux1) = c("AIC")
  list(Estimates = aux, AIC= aux1)
}