varOS: Variance of Order Statistics

In mos: Simulation and Moment Computation for Order Statistics

Variance of Order Statistics

Description

This function computes the variance of order statistics for a given distribution.

Usage

varOS(r, n, dist = c("unif", "exp", "weibull", "tri", "topple"), ...)

Arguments

r	rank(s) of the desired order statistic(s) (e.g., 1 for the smallest order statistic).
n	sample size from which the order statistic is derived.
dist	a character string specifying the name of a distribution. Supported values are: "unif": Uniform distribution "exp": Exponential distribution "weibull": Weibull distribution "tri": Triangular distribution "topple": Topp-Leon distribution
...	further arguments to be passed to dist.

Details

This function computes the variance of the rth order statistic (X_{r:n}) for a given sample size (n) and distribution (dist). The variance is calculated using:

\text{Var}(X_{r:n}) = \text{E}(X^2_{r:n}) - (\text{E}(X_{r:n}))^2

Value

The variance of the rth order statistic.

Examples

# Variance of the 3rd order statistic in a sample of size 10 from a uniform distribution
varOS(r = 3, n = 10, dist = "unif")

mos documentation built on June 16, 2025, 5:09 p.m.