ad2.test: Quadratic Class Anderson-Darling test

In truncgof: GoF tests allowing for left truncated data

Description

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

AD2 = -n +2n log(1-zH) - 1/n sum(1 + 2(n-j) log(1-zj)) + 1/n sum(1-2j) log(zj-zH)

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.

Examples

set.seed(123)
treshold <- 10
xc  <- rlnorm(1000, 2, 2)     # complete sample
xt <- xc[xc >= treshold]      # left truncated sample
ad2.test(xt, "plnorm", list(meanlog = 2, sdlog = 2), H = 10)

Example output

Loading required package: MASS

Attaching package: 'truncgof'

The following object is masked from 'package:stats':

    ks.test


	Quadratic Class Anderson-Darling Test

data:  xt
AD2 = 0.31068, p-value = 0.61

treshold = 10, simulations: 100

truncgof documentation built on May 1, 2019, 10:54 p.m.