spc4sts (version 0.2.1)

exptailecdf: Empirical Cumulative Distribution Function with Exponential Tail Approximation

Description

Computes an empirical cumulative distribution funciton (ecdf) of a given vector of observations, and approximates tails of the ecdf with exponential curves.

Usage

exptailecdf(x, N = max(2, 0.002 * length(x)), m = min(N, 5))

Arguments

x

the given vector of observations

N

the number of observations at each tail of the ecdf used for estimating the exponential curves.

m

the mth observation from each extreme of the ecdf is the starting point to use the estimated exponential curves.

Value

An object of class exptailecdf. See exptailecdf.object

Details

The ecdf has a probability of 0 or 1 for any new observation that lies beyond the range of the data of the cedf. This is a problem when using the ecdf as the reference cdf for the one-sample Anderson-Darling (AD) statistic because the AD statistic is infinite/undefined with such probabilities. The ecdf with exponential tail approximation replaces the tails of the ecdf with exponential curves to solve this problem. The exponential curves are estimated using the observations at the tails of the ecdf. See Bui and Apley (2017) for more details.

References

Bui, A.T., and Apley., D.W. (2017) A Monitoring and Diagnostic Approach for Stochastic Textured Surfaces", Technometrics (in press).

See Also

exptailecdf.object, pexptailecdf, ecdf, ad

Examples

# NOT RUN {
r <- rnorm(1000)
Fr <- exptailecdf(r)
# }