w2.test {truncgof} | R Documentation |
Cram/'er-von Mises 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 |
estfun |
an function as character string or |
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
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 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 |
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)