This function computes the skewness of the order statistics for a given distribution.
Usage
skewOS(r, n, dist = c("unif", "exp", "weibull", "tri"), ...)
Value
The skewness 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
...
further arguments to be passed to dist.
Details
The skewness of the \(r\)th order statistic is calculated using the formula:
$$\text{Skewness}(X_{r:n}) = \text{E}(\frac{X_{r:n}-\mu_{r:n}} {\sigma_{r:n}})^3$$
where \(\mu_{r:n}\) and \(\sigma_{r:n}\) are the mean and standard deviation of the \(r\)th order statistic, respectively.