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stats_from_distribution <- function(binFit) {
PDF <- binFit[[1]]
CDF <- binFit[[2]]
E <- binFit[[3]]
cdf_mean <- E - pracma::integral(CDF, 0, E)
v <- pracma::integral(function(x){2*x-2*x*CDF(x)}, 0 ,E) - cdf_mean^2
g <- 1-pracma::integral(function(x){(1-CDF(x))^2}, 0, E)/cdf_mean
t <- pracma::integral(function(x){PDF(x)*x/cdf_mean*log(x/cdf_mean)}, 0, E)
statistics <- c(cdf_mean, v, sqrt(v), g, t)
names(statistics) <- c("mean", "variance", "SD", "Gini", "Theil")
return(statistics)
}
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