AndersonDarlingTest.RdPerforms the Anderson-Darling test of goodness-of-fit to a specified continuous univariate probability distribution.
AndersonDarlingTest(x, null = "punif", ..., nullname)numeric vector of data values.
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.
optional character string describing the null distribution.
The default is "uniform distribution".
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).
An object of class "htest" representing the result of
the hypothesis test.
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)
#>
#> Anderson-Darling test of goodness-of-fit
#> Null hypothesis: Normal distribution
#> with parameters mean = 2.000, sd = 1.000
#>
#> data: x
#> An = 0.47535, p-value = 0.768
#>