order_gammag {orders}

Random Sampling of k-th Order Statistics from a Gamma Uniform G Distribution

Description

order_gammag is used to obtain a random sample of the k-th order statistic from a Gamma Uniform G distribution.

Usage

order_gammag(size, spec, a, k, n, p = 0.5, 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.

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.

p

numeric, represents the 100p percentile for the distribution of the k-th order statistic. Default value is population median, p = 0.5.

alpha

numeric, (1 - alpha) represents the confidence of an interval for the population percentile p 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 Gamma Uniform G Distribution, the value of its join probability density function evaluated in the random sample and an approximate (1 - alpha) confidence interval for the population percentile p of the distribution of the k-th order statistic.

Author(s)

Carlos Alberto Cardozo Delgado <[e-mail]>.

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

library(orders)
# A sample of size 10 of the 3-th order statistics from a Gamma Uniform Exponential Distribution
order_gammag(10,"exp",1,k=3,n=50,p=0.5,alpha=0.02)
# A sample of size 10 of the 3-th order statistics from a Gamma Uniform Normal Distribution
order_gammag(10,"norm",1,k=3,n=50,p=0.5)
# A sample of size 10 of the 3-th order statistics from a Gamma Uniform Log-normal Distribution
order_gammag(10,"lnorm",1,k=3,n=50,p=0.5)
# A sample of size 10 of the 3-th order statistics from a Gamma Uniform Chi-square Distribution
order_gammag(10,"chisq",1,k=3,n=50,p=0.5,df=3)