kurtOS: Kurtosis of Order Statistics

In mos: Simulation and Moment Computation for Order Statistics

Kurtosis of Order Statistics

Description

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

Usage

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

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 kurtosis of the rth order statistic is calculated using the formula:

\text{kurtosis}(X_{r:n}) = \text{E}(\frac{X_{r:n}-\mu_{r:n}} {\sigma_{r:n}})^4

where \mu_{r:n} and \sigma_{r:n} are the mean and standard deviation of the rth order statistic, respectively.

Value

The kurtosis of the rth order statistic.

See Also

varOS, skewOS

Examples

# Compute the kurtosis of the 3rd order statistic from a sample of size 10
kurtOS(r = 3, n = 10, dist = "unif")

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