# Random Sampling of K-th Order Statistics from a Generalized Log-gamma Distribution `order_glg` is used to obtain a random sample of the K-th order statistics from a generalized log-gamma distribution. ```r order_glg(size, mu, sigma, lambda, k, n, alpha = 0.05) ``` ## Arguments - `size`: numeric, represents the size of the sample. - `mu`: numeric, represents the location parameter. Default value is 0. - `sigma`: numeric, represents the scale parameter. Default value is 1. - `lambda`: numeric, represents the shape parameter. Default value is 1. - `k`: numeric, represents the K-th smallest value from a sample. - `n`: numeric, represents the size of the sample to compute the order statistic from. - `alpha`: numeric, (1 - alpha) represents the confidence of an interval for the population median of the distribution of the k-th order statistic. Default value is 0.05. ## Returns A list with a random sample of order statistics from a generalized log-gamma distribution, the value of its join probability density function evaluated in the random sample and a (1 - alpha) confidence interval for the population median of the distribution of the k-th order statistic. ## Examples ```r # A random sample of size 10 of order statistics from a Extreme Value Distribution. order_glg(10,0,1,1,1,50) ## Not run: # A small comparison between two random sampling methods of order statistics # Method 1 m <- 10 output <- rep(0,m) order_sample <- function(m,n,k){ for(i in 1:m){ sample <- rglg(n) order_sample <- sort(sample) output[i] <- order_sample[k] } return(output) } N <- 10000 n <- 200 k <- 100 system.time(order_sample(N,n,k)) sample_1 <- order_sample(N,n,k) hist(sample_1) summary(sample_1) # Method 2 system.time(order_glg(N,0,1,1,k,n)) sample_2 <- order_glg(N,0,1,1,k,n)$sample hist(sample_2) summary(sample_2) ## End(Not run) ``` ## References Gentle, J, Computational Statistics, First Edition. Springer - Verlag, 2009. Naradajah, S. and Rocha, R. (2016) Newdistns: An R Package for New Families of Distributions, Journal of Statistical Software. ## Author(s) Carlos Alberto Cardozo Delgado .

order_glg function