mos (version 0.1.3)

kurtOS: 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"), ...)

Value

The kurtosis 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 kurtosis of the \(r\)th 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 \(r\)th order statistic, respectively.

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")