# R/order_eg.R In orders: Sampling from k-th Order Statistics of New Families of Distributions

#### Documented in order_eg

```#' Random Sampling of k-th Order Statistics from a Exponentiated Generalized G Distribution
#'
#'\code{order_eg} is used to obtain a random sample of k-th order order statistic from a Exponentiated Generalized G Distribution.
#' @param size numeric, represents the size of the sample.
#' @param spec character, represents an specific G distribution. Possible values "norm", "exp","lnorm","chisq".
#' @param a numeric, represents the first shape parameter. Default value is 1.
#' @param b numeric, represents the second shape parameter. Default value is 1.
#' @param k numeric, represents the Kth smallest value from a sample.
#' @param n numeric, represents the size of the sample to compute the order statistic from.
#' @param 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.
#' @param ... represents others parameters of the G distribution.
#' @return A list with a random sample of order statistics from a Exponentiated Generalized G Distribution, the value of its join probability density function evaluated in the random sample
#' a (1 - alpha) confidence interval for the population median of the distribution of the k-th order statistic.
#' @references Gentle, J, Computational Statistics, First Edition. Springer - Verlag, 2009.
#' @references Naradajah, S. and Rocha, R. (2016) Newdistns: An R Package for New Families of Distributions, Journal of Statistical Software.
#' @author Carlos Alberto Cardozo Delgado <cardozorpackages@gmail.com>.
#' @examples
#' library(orders)
#' # A sample of size 10 of the 3-th order statistics from
#' # a Exponentiated Generalized Exponential Distribution
#' order_eg(10,"exp",1,1,k=3,50,alpha=0.02)
#' # A sample of size 10 of the 3-th order statistics from
#' # a Exponentiated Generalized Normal Distribution
#' order_eg(10,"norm",1,1,k=3,50)
#' # A sample of size 10 of the 3-th order statistics from
#' # a Exponentiated Generalized Log-normal Distribution
#' order_eg(10,"lnorm",1,1,k=3,50)
#' # A sample of size 10 of the 3-th order statistics from
#' # a Exponentiated Generalized Chi-square Distribution
#' order_eg(10,"chisq",1,1,k=3,50,df=3)
#' @importFrom Newdistns qeg deg
#' @importFrom stats rbeta
#' @export order_eg

order_eg <- function(size,spec,a,b,k,n,alpha=0.05,...){
sample  <- qeg(initial_order(size,k,n),spec,a,b,...)
pdf     <- factorial(size)*cumprod(deg(sample,spec,a,b,...))[size]
if(size>5){
return(list(sample=sample,pdf=pdf,ci_median=interval_median(size,sample,alpha)))
}
cat("---------------------------------------------------------------------------------------------\n")
cat("We cannot report the confidence interval. The size of the sample is less or equal than five.\n")
return(list(sample=sample,pdf=pdf))
}
```

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orders documentation built on July 17, 2021, 9:08 a.m.