Cram/'er-von Mises test providing a comparison of a fitted distribution
with the empirical distribution.
Usage
w2.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.
Value
A list with class "mchtest" containing the following components
statistic
the value of the Cram\'er-von Mies 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 "Cramer-von Mises test"
sim.no
number of simulated szenarios in the Monte-Carlo simulation
Details
The Cram/'er-von Mies 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
$$W^2 = \frac{n}{3} + \frac{n z_H}{1-z_H} +
\frac{1}{n(1-z_H)}\sum_{j=1}^n(1-2j)z_j + \frac{1}{(1-z_H)^2}\sum_{j=1}^{n}(z_j-z_H)^2$$
with $z_H = F_theta(H)$ and $
z_j=F_theta(x_j)$, where $x_1, \dots, x_n$ are the ordered data values. Here,
$F_theta$ is the null distribution.
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