R/cdf.size.total.R

In mhweber/spsurvey: Spatial Survey Design and Analysis

################################################################################
# Function: cdf.size.total
# Programmer: Tom Kincaid
# Date: July 12, 2000
# Last Revised: June 3, 2008
#
#' Size-weighted Cumulative Distribution Funcition Estimate for Total
#'
#' This function calculates an estimate of the size-weighted cumulative
#' distribution function (CDF) for the total of a finite resource.  The set of
#' values at which the CDF is estimated is supplied to the function.  If the
#' known sum of the size-weights of the resource is provided, the classic ratio
#' estimator is used to calculate the estimate. That estimator is the product of
#' the known sum of the size-weights of the resource and the Horvitz- Thompson
#' ratio estimator, where the latter is the ratio of two Horvitz- Thompson
#' estimators.  The numerator of the ratio estimates the size-weighted total of
#' the resource equal to or less than a specified value.  The denominator of the
#' ratio estimates the sum of the size-weights of the resource.  If the known
#' sum of the size-weights of the resource is not provided, the Horvitz-Thompson
#' estimator of the size-weighted total of the resource equal to or less than a
#' specified value is used to calculate the estimate.  The function can
#' accomodate single-stage and two-stage samples.
#'
#' @param z Vector of the response value for each site.
#'
#' @param wgt Vector of the final adjusted weight (inverse of the sample
#'   inclusion probability) for each site, which is either the weight for a
#'   single- stage sample or the stage two weight for a two-stage sample.
#'
#' @param val Vector of the set of values at which the CDF is estimated.
#'
#' @param cluster.ind Logical value that indicates whether the sample is a
#'   two- stage sample, where TRUE = a two-stage sample and FALSE = not a
#'   two-stage sample.
#'
#' @param cluster Vector of the stage one sampling unit (primary sampling unit
#'   or cluster) code for each site.
#'
#' @param wgt1 Vector of the final adjusted stage one weight for each site.
#'
#' @param popsize Known size of the resource, which is used to perform ratio
#'   adjustment to estimators expressed using measurement units for the
#'   resource.  For a finite resource, this argument is either the total number
#'   of sampling units or the known sum of size-weights.  For an extensive
#'   resource, this argument is the measure of the resource, i.e., either known
#'   total length for a linear resource or known total area for an areal
#'   resource.  For a stratified sample this variable must be a vector
#'   containing a value for each stratum and must have the names attribute set
#'   to identify the stratum codes.
#'
#' @param swgt Vector of the size-weight for each site, which is the stage two
#'   size-weight for a two-stage sample.
#'
#' @param swgt1 Vector of the stage one size-weight for each site.
#'
#' @return The size-weighted CDF estimate.
#'
#' @author Tom Kincaid \email{Kincaid.Tom@epa.gov}
#'
#' @keywords survey
#'
#' @export
################################################################################

cdf.size.total <- function(z, wgt, val, cluster.ind, cluster, wgt1, popsize,
   swgt, swgt1) {

# Calculate additional required values

   m <- length(val)
   wgt <- wgt*swgt
   if(cluster.ind) {
      cluster <- factor(cluster)
      ncluster <- length(levels(cluster))
      z.lst <- split(z, cluster)
      wgt2.lst <- split(wgt, cluster)
      wgt1 <- wgt1*swgt1
      wgt1.u <- as.vector(tapply(wgt1, cluster, unique))
   }

# Calculate the cdf estimate

   cdf <- numeric(m)
   if(cluster.ind) {
      for(i in 1:m) {
         temp <- numeric(ncluster)
         for(j in 1:ncluster) {
            temp[j] <- sum(ifelse(z.lst[[j]] <= val[i], wgt2.lst[[j]], 0))
         }
         cdf[i] <- sum(wgt1.u*temp)
      }
   } else {
      for(i in 1:m) {
         cdf[i] <- sum(ifelse(z <= val[i], wgt, 0))
      }
   }

# Adjust the estimate when the sum of the size-weights of the resource is known

   if(!is.null(popsize)) {
      if(cluster.ind)
         cdf <- popsize*(cdf/sum(wgt1*wgt))
      else
         cdf <- popsize*(cdf/sum(wgt))
   }

# Return the estimate

   cdf
}