R/funny_estimators.R

In mikeroswell/MeanRarity: Hill Diversity Estimation and Visualization

#funny estimators

#' Bad estimate of relative abundance with an incorrect finite-size correction
#'
#' @param x A numeric vector of species abundances
#'
#' @return An incorrect estimate of relative abundance
#'
#' @noRd
fsr<-function(x){
  (x-0.8)/(sum(x)-0.8)
}


#' Incorrect diversity estimator based on finite-size fudge
#'
#' This is a riff on \code{\link{dfun}} that uses \code{\link{fsr}}, which is not the correct way to deal with finite
#' size corrections, though it is similar to E.H. Simpson's estimator. Rather than subtracting 1, though, it subtracts 0.8
#'
#' @template ab_template
#' @template l_template
#' @template q_template
#'
#' @return Incorrect estimate of Hill Diversity with a goofy bias correction term (a scalar)
#'
#' @seealso \code{\link{rarity}}
#'
#' @noRd
fsd<-function(ab, l, q = NULL){
  if(!is.null(q)){
    l = 1 - q
    warning("l has been set to 1-q")
  }
  ab <- ab[ab != 0]
  rp <- ab/sum(ab)
  fs <- fsr(ab)
  if(l == 0) {return(exp(sum(rp * log(1/fs))))}
  return(sign(l) * ipfun(sign(l) * sum(rp * pfun(1/fs, l)),l))
}

#' Simpson's estimator of Hill-Simpson Diversity (we think?)
#'
#' E.H. Simpson's 1949 estimator of Simpson's Concentration is an unbiased
#' estimator. It is not an unbiased Hill-Simpson estimator, but it is a pretty
#' good one
#'
#' @param ab Numeric vector of species abundances
#'
#' @return the reciprocal of the Simpson's concentration, a low-bias estimator for Hill-Simpson diversity (scalar)
#' @noRd
hill_simpson_estimator <- function(ab){
  n <- sum(ab)
  return(1/(
    sum(ab/n) * ((ab - 1)/(n - 1)))
  )
}