w2.test: Cram/'er-von Mises test
In truncgof: GoF tests allowing for left truncated data

Description Usage Arguments Details Value References See Also Examples

Cram/'er-von Mises test providing a comparison of a fitted distribution with the empirical distribution.

1	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 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)