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

`AndersonDarlingTest(x, null = "punif", ..., nullname)`

An object of class `"htest"`

representing the result of
the hypothesis test.

- 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.

- nullname
optional character string describing the null distribution.

The default is`"uniform distribution"`

.

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

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.

The procedures currently implemented are for the case of a SIMPLE null hypothesis, that is, where all the parameters of the distribution are known. Note that other packages such as 'normtest' support the test of a COMPOSITE null hypothesis where some or all of the parameters are unknown leading to different results concerning the test statistic and the p-value. Thus in 'normtest' you can test whether the data come from a normal distribution with some mean and variance (which will be estimated from the same data).

The discrepancies can be large if you don't have a lot of data (say less than 1000 observations).

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.

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

`shapiro.test`

and all other tests for normality.

```
x <- rnorm(10, mean=2, sd=1)
AndersonDarlingTest(x, "pnorm", mean=2, sd=1)
```

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