orders (version 0.1.8)

order_gpareto: Random Sampling of k-th Order Statistics from a Generalized Pareto Distribution

Description

order_gpareto is used to obtain a random sample of the k-th order statistic from a Generalized Pareto distribution and some associated quantities of interest.

Usage

order_gpareto(size, k, shape1, shape2, scale, n, p = 0.5, alpha = 0.05, ...)

Value

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

Arguments

size

numeric, represents the size of the sample.

k

numeric, represents the k-th smallest value from a sample.

shape1

numeric, represents a first shape parameter value. Must be strictly positive.

shape2

numeric, represents a second shape parameter value. Must be strictly positive.

scale

numeric, represents scale parameter values. Must be strictly positive.

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 a Generalized Pareto distribution.

Author

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

References

Gentle, J, Computational Statistics, First Edition. Springer - Verlag, 2009.

Klugman, S. A., Panjer, H. H. and Willmot, G. E. (2012), Loss Models, From Data to Decisions, Fourth Edition, Wiley.

Examples

library(orders)
# A sample of size 10 of the 3-th order statistics from a Generalized Pareto Distribution
order_gpareto(size=10,shape1=0.75,shape2=1,scale=0.5,k=3,n=50,p=0.5,alpha=0.02)