Quadratic class Anderson-Darling test providing a comparison of a fitted distribution
with the empirical distribution.
Usage
ad2.test(x, distn, fit, H = NA, 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
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 Anderson-Darling test compares the null distribution with the empirical distribution
function of the observed data, where left truncated data samples are allowed.
The test statistic is given by
with z_H = F_theta(H) and
z_j=F_theta(x_j), 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 Quadratic Class 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 "Quadratic Class Anderson-Darling test"
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
See Also
ad2up.test, w2.test for other quadratic class tests
and ks.test, v.test, adup.test, ad.test
for supremum class tests. For more details see mctest.