# order_gbg: Random Sampling of k-th Order Statistics from a Generalized... In orders: Sampling from k-th Order Statistics of New Families of Distributions

## Description

`order_gbg` is used to obtain a random sample of the k-th order statistic from a Generalized Beta G distribution and some associated quantities of interest.

## Usage

 `1` ```order_gbg(size, spec, a, b, c, k, n, alpha = 0.05, ...) ```

## Arguments

 `size` numeric, represents the size of the sample. `spec` character, represents an specific G distribution. Possible values "norm", "exp","lnorm","chisq". `a` numeric, represents the first shape parameter. Default value is 1. `b` numeric, represents the second shape parameter. Default value is 1. `c` numeric, represents the third shape parameter. Default value is 1. `k` numeric, represents the Kth 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. `...` represents others parameters of the G distribution.

## Value

A list with a random sample of order statistics from a Generalized Beta G 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.

## 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.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```library(orders) # A sample of size 10 of the 3-th order statistics from # a Generalized Beta Exponential Distribution order_gbg(10,"exp",1,1,1,k=3,50,alpha=0.02) # A sample of size 10 of the 3-th order statistics from # a Generalized Beta Normal Distribution order_gbg(10,"norm",1,1,1,k=3,50) # A sample of size 10 of the 3-th order statistics from # a Generalized Beta Log-normal Distribution order_gbg(10,"lnorm",1,1,1,k=3,50) # A sample of size 10 of the 3-th order statistics from # a Generalized Beta Chi-square Distribution order_gbg(10,"chisq",1,1,1,k=3,50,df=3) ```

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