r - Logarithmic mean of vector -

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to follow exact methodology presented in article calculate logarithmic mean of data vector. did not find functions in r, or previous discussions. case 2 numbers clear, not work out efficient method calculate log mean large vector of numbers. suggestions?

# calculating different types of means  # data dat <- c(0.008845299, 0.040554701)  # arithmetic mean arith.m <- mean(dat)  # logarithmic mean # http://en.wikipedia.org/wiki/logarithmic_mean log.m <- (dat[1] - dat[2])/(log(dat[1])-log(dat[2]))  # geometric mean # http://stackoverflow.com/questions/2602583/geometric-mean-is-there-a-built-in geo_mean <- function(data) {   log_data <- log(data)   gm <- exp(mean(log_data[is.finite(log_data)]))   return(gm) }  geo.m <- geo_mean(dat)  # show arithmetic > logarithmic > geometric arith.m; log.m; geo.m  # how calculate logarithmic mean vector? dat.n <- c(0.008845299, 0.040554701, 0.047645299, 0.036654701, 0.017345299, 0.018754701, 0.032954701, 0.043145299, 0.026845299, 0.033054701, 0.025554701)

update calculation strips out 0 values (but, pointed out below valid?):

# add low number (generally considered 0 in r) nzero <- 1.940656e-324 dat.n <- c(dat.n, nzero)  # arithmetic mean arith.m <- mean(dat.n)  geo_mean <- function(data) {   log_data <- log(data)   gm <- exp(mean(log_data[is.finite(log_data)]))   return(gm) }  geo.m <- geo_mean(dat.n)  lmv <- function(x){   ddlog <- function(x){     d <- rep(0, length(x))     (i in 1:length(x)){       d[i] <- prod(x[i] - x[-i])     }     sum(log(x)[is.finite(log(x))]/d[is.finite(log(x))])   }   n <- length(x[which(x>0)]) - 1   ((-1)^(n+1)*n*ddlog(x))^(-1/n) }  log.m <- lmv(dat.n)  # show arithmetic > logarithmic > geometric arith.m; log.m; geo.m

followed wiki (generalized (n+1) values):

http://en.wikipedia.org/wiki/divided_difference#expanded_form

http://en.wikipedia.org/wiki/logarithmic_mean#mean_value_theorem_of_differential_calculus_2 

ddlog <- function(x){   d <- rep(0, length(x))   (i in 1:length(x)){     d[i] <- prod(x[i] - x[-i])   }   sum(log(x)/d) }  # ddlog divided difference of logarithm.  lmv <- function(x){   n <- length(x) - 1   ((-1)^(n+1)*n*ddlog(x))^(-1/n) }  r > <- c(0.008845299, 0.040554701, 0.047645299, 0.036654701, 0.017345299, 0.018754701, 0.032954701, 0.043145299, 0.026845299, 0.033054701, 0.025554701) r >  r > lmv(a) [1] 0.0277

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