| w2.test {truncgof} | R Documentation |
Cramér-von Mise test providing a comparison of a fitted distribution with the empirical distribution.
w2.test(x, distn, fit, H = NA, sim = 100, tol = 1e-04, estfun = NA)
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. |
The Cramér-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
W2 = n/3 + n zH/(1-zH) + 1/(n (1-zH)) sum((1-2j) zj) + 1/(1-zH)^2 sum(zj-zH)^2
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.
A list with class "mchtest" containing the following components
statistic |
the value of the Cramér-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 Mies test" |
sim.no |
number of simulated szenarios in the Monte-Carlo simulation |
Chernobay, A., Rachev, S., Fabozzi, F. (2005), Composites goodness-of-fit tests for left-truncated loss samples, Tech. rep., University of Calivornia Santa Barbara
ad2up.test, ad2.test for other quadratic class tests
and ks.test, v.test, adup.test, ad.test
for supremum class tests. For more details see mctest.
set.seed(123) treshold <- 10 xc <- rlnorm(100, 2, 2) # complete sample xt <- xc[xc >= treshold] # left truncated sample w2.test(xt, "plnorm", list(meanlog = 2, sdlog = 2), H = 10)