ad.test: Supremum Class Anderson-Darling test

In truncgof: GoF tests allowing for left truncated data

Description

Supremum class version of the Anderson-Darling test providing a comparison of a fitted distribution with the empirical distribution.

Usage

ad.test(x, distn, fit, H = NA, 
        alternative = c("two.sided", "less", "greater"), 
        sim = 100, tol = 1e-04, estfun = NA)

Arguments

x	a numeric vector of data values
distn	character string naming the null distribution function
fit	list of null distribution parameters
H	a treshold value
alternative	indicates the alternative hypothesis and must be one of "two.sided" (default), "less", or "greater". Initial letter must be specified only.
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 stops
estfun	an function as character string or NA (default). See mctest.

Details

The supremum class Anderson-Darling test compares the null distribution with the empirical distribution of the observed data. The test statistic is given by

AD+ = sqrt(n) sup((zH + j/n (1-zH) -zj)/sqrt((zj-zH)(1-zj))

AD+ = sqrt(n) sup(zj - (zH + (j-1)/n (1-zH)))/sqrt((zj-zH)(1-zj))

AD = max(AD+, AD-).

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 Supremum 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 "Supremum Class Anderson-Darling test"
alternative	the alternative
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

ks.test, v.test, adup.test for other supremum class tests and ad2.test, ad2up.test, w2.test for quadratic class tests. For more details see mctest.

Examples

set.seed(123)
treshold <- 10
xc  <- rlnorm(100, 2, 2)    # complete sample
xt <- xc[xc >= treshold]    # left truncated sample
ad.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


	Supremum Class Anderson-Darling Test

data:  xt
AD = 3.124, p-value = 0.12
alternative hypothesis: two.sided

treshold = 10, simulations: 100

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