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#' Calculate the Mean Relative Difference for Two Probability Density Distributions
#'
#' This function calculates the mean relative difference for two probability density
#' distributions expressed as Smooth Density Histograms.
#'
#' @param vector1 A numeric vector representing the first probability density distribution.
#' @param vector2 A numeric vector representing the second probability density distribution.
#'
#' @return The mean relative difference between the two probability density distributions.
#'
#' @importFrom SmoothDensHist1dim SmoothDensHist1dim
#'
amrdd <- function(vector1, vector2) {
# Combine the two input vectors and create a Smooth Density Histogram
densA <- SmoothDensHist1dim(c(vector1, vector2))
xA <- densA$Kernels
# Create Smooth Density Histograms for each input vector
dens1 <- SmoothDensHist1dim(x = vector1, KernelsOrNbins = xA)
dens2 <- SmoothDensHist1dim(x = vector2, KernelsOrNbins = xA)
# Merge the Smooth Density Histograms into a single data frame
dfPDF <- data.frame(
Kernels = xA,
SDH.x = dens1$SDH,
SDH.y = dens2$SDH
)
# Calculate the absolute difference and the mean of the two distributions
dfPDF$Diff <- abs(dfPDF$SDH.x - dfPDF$SDH.y)
dfPDF$Mean <- (dfPDF$SDH.x + dfPDF$SDH.y) / 2
dfPDF$Mean[dfPDF$Mean == 0] <- 1
# Calculate the relative difference and return the mean
dfPDF$RelDiff <- dfPDF$Diff / dfPDF$Mean
return(mean(dfPDF$RelDiff, na.rm = TRUE))
}
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