# 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

 `1` ```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

`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

 ```1 2 3 4 5``` ```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