#' Empirical Distribution function with cluster weights psi
#'
#' @param data The data, provided as a list of lists
#' @param type Character, specifying whether weighted or unweighted estimator will be used. Defaults to unweighted. The first letter is enough.
#' @return A list of vectors with the weights.
weight_fun = function(data, type = "unweighted"){
psi = list()
theta = numeric(length(data))
if(type == "unweighted" || type == "u"){
for(i in 1:length(data)){
psi[[i]] = rep(1 / length(data[[i]]), length(data[[i]]))
}
theta = rep(1/length(data), length(data))
}
if(type == "weighted" || type == "w"){
for(i in 1:length(data)){
psi[[i]] = sapply(data[[i]], FUN = function(x) {
length(x) / sum(sapply(data[[i]], length))
})
}
theta = sapply(data, FUN = function(x){
length(x) / sum(sapply(data, length))
})
}
return(list("theta" = theta, "psi" = psi))
}
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