This function computes the variance of order statistics for a given distribution.
Usage
varOS(r, n, dist = c("unif", "exp", "weibull", "tri", "topple"), ...)
Value
The variance of the \(r\)th order statistic.
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 \(r\)th order statistic (\(X_{r:n}\))
for a given sample size (n) and distribution (dist). The variance is calculated using:
$$\text{Var}(X_{r:n}) = \text{E}(X^2_{r:n}) - (\text{E}(X_{r:n}))^2$$