# ad.test: Anderson-Darling Test of Goodness-of-Fit In baddstats/goftest: Classical Goodness-of-Fit Tests for Univariate Distributions

## Description

Performs the Anderson-Darling test of goodness-of-fit to a specified continuous univariate probability distribution.

## Usage

 `1` ```ad.test(x, null = "punif", ..., estimated=FALSE, nullname) ```

## Arguments

 `x` Numeric vector of data values. `null` A function, or a character string giving the name of a function, to compute the cumulative distribution function for the null distribution. `...` Additional arguments for the cumulative distribution function. `estimated` Logical value indicating whether the parameters of the distribution were estimated using the data `x` (composite null hypothesis), or were fixed in advance (simple null hypothesis, the default). `nullname` Optional character string describing the null distribution. The default is `"uniform distribution"`.

## Details

This command performs the Anderson-Darling test of goodness-of-fit to the distribution specified by the argument `null`. It is assumed that the values in `x` are independent and identically distributed random values, with some cumulative distribution function F. The null hypothesis is that F is the function specified by the argument `null`, while the alternative hypothesis is that F is some other function.

By default, the test assumes that all the parameters of the null distribution are known in advance (a simple null hypothesis). This test does not account for the effect of estimating the parameters.

If the parameters of the distribution were estimated (that is, if they were calculated from the same data `x`), then this should be indicated by setting the argument `estimated=TRUE`. The test will then use the method of Braun (1980) to adjust for the effect of parameter estimation.

Note that Braun's method involves randomly dividing the data into two equally-sized subsets, so the p-value is not exactly the same if the test is repeated. This technique is expected to work well when the number of observations in `x` is large.

## Value

An object of class `"htest"` representing the result of the hypothesis test.

## Author(s)

Original C code by George Marsaglia and John Marsaglia. R interface by Adrian Baddeley.

## References

Anderson, T.W. and Darling, D.A. (1952) Asymptotic theory of certain 'goodness-of-fit' criteria based on stochastic processes. Annals of Mathematical Statistics 23, 193–212.

Anderson, T.W. and Darling, D.A. (1954) A test of goodness of fit. Journal of the American Statistical Association 49, 765–769.

Braun, H. (1980) A simple method for testing goodness-of-fit in the presence of nuisance parameters. Journal of the Royal Statistical Society 42, 53–63.

Marsaglia, G. and Marsaglia, J. (2004) Evaluating the Anderson-Darling Distribution. Journal of Statistical Software 9 (2), 1–5. February 2004. http://www.jstatsoft.org/v09/i02

`pAD` for the null distribution of the test statistic.
 ```1 2 3``` ```x <- rnorm(10, mean=2, sd=1) ad.test(x, "pnorm", mean=2, sd=1) ad.test(x, "pnorm", mean=mean(x), sd=sd(x), estimated=TRUE) ```