order_fellerpareto {orders}

Random Sampling of k-th Order Statistics from a Feller-Pareto Distribution

Description

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

Usage

order_fellerpareto(
  size,
  k,
  min,
  shape1,
  shape2,
  shape3,
  scale,
  n,
  p = 0.5,
  alpha = 0.05,
  ...
)

Arguments

size

numeric, represents the size of the sample.

k

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

min

numeric, represents the lower bound of the support of the distribution.

shape1

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

shape2

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

shape3

numeric, represents a third 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 Feller-Pareto distribution.

Value

A list with a random sample of order statistics from a Feller-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.

Author(s)

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 Feller-Pareto Distribution
order_fellerpareto(size=10,
                   min=0.5,shape1=0.75,shape2=1,shape3=1.25,scale=0.5,k=3,n=50,p=0.5,alpha=0.02)