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```
#' @title Fractional Bias (FB)
#' @author Thi-Thu-Hong Phan, Andre Bigand, Emilie Poisson-Caillault
#' @description Calculate the FB between two univariate signals Y (imputed values) and X (true values).
#' @details
#' This function returns the FB value of two vectors univariate signals. This indicator indicates whether predicted values are underestimated or overestimated compared to true values.
#' A perfect imputation model has \eqn{FB = 0}.
#' An imputation model is acceptable when its FB value is less than or equal to 0.3 (\eqn{FB <= 0.3}).
#' The two vectors Y and X are the same length, on the contrary an error will be displayed.
#' In both input vectors, eventual NA will be exluded with a warning diplayed.
#' @param Y vector of imputed values
#' @param X vector of true values
#' @param verbose if TRUE, print advice about the quality of the model
#' @examples
#' data(dataFSMUMI)
#' X <- dataFSMUMI[, 1] ; Y <- dataFSMUMI[, 2]
#' compute.fb(Y,X)
#' compute.fb(Y,X, verbose = TRUE)
#'
#' # If mean(X)=mean(Y)=0, it is impossible to estimate FB,
#' # unless both true and imputed values vectors are constant.
#' # By definition, in this case, FB = 0.
#' X <- rep(0, 10) ; Y <- rep(0, 10)
#' compute.fb(Y,X)
#'
#' # If true and imputed values are not zero and are opposed, FB = Inf.
#' X <- rep(runif(1), 10)
#' Y <- -X
#' compute.fb(Y,X)
compute.fb<-function(Y, X,verbose=F){
if(length(Y)!=length(X)){stop("Input vectors are of different length !!!")}
lengthNAX <- sum(is.na(X)) # Number of NA values
if(lengthNAX > 0){warning(paste("Vector of true values contains ", lengthNAX, " NA !!! NA excluded", sep = ""))}
lengthNAY <- sum(is.na(Y)) # Number of NA values
if(lengthNAY > 0){warning(paste("Vector of imputed values contains ", lengthNAY, " NA !!! NA excluded", sep = ""))}
m1=mean(Y, na.rm= T)
m2=mean(X, na.rm = T)
if(m1!=0&&m1==-m2){warning("X=-Y => FB=Inf")}
if(m1==0&&m2==0){
if((max(Y, na.rm = T)-min(Y, na.rm = T))==(max(X, na.rm = T)-min(X, na.rm = T))){
warning("Vectors of input and imputed values are equal and constant. By definition FB=0")
FB <- 0
if(verbose){print("acceptable FB")}
out<-FB
}
else{stop(print("Impossible to estimate FB: vectors of input and imputed values have the same mean 0 but are not constant !!!"))}
}
else{
FB <- 2*abs((m1-m2)/(m1+m2))
if (verbose){
if(abs(FB)<0.3) {print("acceptable FB")
}else{print("non acceptable FB")}
}
out<- FB
}
return(out)
}
```

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