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Last data update: 2014.03.03

R: Supremum Class Upper Tail Anderson-Darling test

adup.test

R Documentation

Supremum Class Upper Tail Anderson-Darling test

Description

Supremum class version of the Upper Tail Anderson-Darling test providing a comparison of a fitted distribution with the empirical distribution.

Usage

adup.test(x, distn, fit, H = NA, 
          alternative = c("two.sided", "less", "greater"), 
          sim = 100, tol = 1e-04, estfun = NA)

Arguments

`x`	a numeric vector of data values
`distn`	character string naming the null distribution
`fit`	list of null distribution parameters
`H`	a treshold value
`alternative`	indicates the alternative hypothesis and must be one of "two.sided" (default), "less", or "greater". Initial letter must be specified only.
`sim`	maximum number of szenarios in the Monte-Carlo simulation
`tol`	if the difference of two subsequent p-value calculations is lower than `tol` the Monte-Carlo simulation is discontinued
`estfun`	an function as character string or `NA` (default). See `mctest`.

Details

The supremum class Upper Tail Anderson-Darling test compares the null distribution with the empirical distribution function of the observed data. The test statistic is given by

ADup+ = sqrt(n) sup((j/n - zj)/(1 - zj))

ADup- = sqrt(n) sup((zj - (j-1)/n)/(1 - zj))

ADup = max(ADup+, ADup-)

with zH=F_theta(H) and zj=F_theta(xj), where x_1, …, x_n are the ordered data values. Here, F_theta is the null distribution.

Value

A list with class "mchtest" containing the following components

`statistic`	the value of the Supremum Class Upper Tail Anderson-Darling statistic
`treshold`	the treshold value
`p.value`	the p-value of the test
`data.name`	a character string giving the name of the data
`method`	the character string "Supremum Class Upper Tail Anderson-Darling test"
`alternative`	the alternative
`sim.no`	number of simulated szenarios in the Monte-Carlo simulation

References

Chernobay, A., Rachev, S., Fabozzi, F. (2005), Composites goodness-of-fit tests for left-truncated loss samples, Tech. rep., University of Calivornia Santa Barbara

Examples

set.seed(123)
treshold <- 10
xc  <- rlnorm(100, 2, 2)     # complete sample
xt <- xc[xc >= treshold]     # left truncated sample
adup.test(xt, "plnorm", list(meanlog = 2, sdlog = 2), H = 10)