order_sm: Random Sampling of k-th Order Statistics from a Singh-Maddala...
In orders: Sampling from k-th Order Statistics of New Families of Distributions

order_sm

R Documentation

Random Sampling of k-th Order Statistics from a Singh-Maddala Distribution

Description

order_sm is used to obtain a random sample of the k-th order statistic from a Singh-Maddala distribution and some associated quantities of interest.

Usage

order_sm(size, k, shape1, shape2, 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.
`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 Singh-Maddala distribution.

Value

A list with a random sample of order statistics from a Singh-Maddala 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 <cardozorpackages@gmail.com>.

References

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

Kleiber, C. and Kotz, S. (2003). Statistical Size Distributions in Economics and Actuarial Sciences, Hoboken, NJ, USA: Wiley-Interscience.

Examples

library(orders)
# A sample of size 10 of the 3-th order statistics from a Singh-Maddala Distribution
order_sm(size=10,shape1=1,shape2=2,scale=1,k=3,n=50,p=0.5,alpha=0.02)

orders documentation built on Nov. 14, 2023, 9:07 a.m.