order_glg function

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.

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

# 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 cardozorpackages@gmail.com.