R: Null Distribution of Anderson-Darling Test Statistic

pAD {goftest} | R Documentation

## Null Distribution of Anderson-Darling Test Statistic

### Description

`pAD` computes the cumulative distribution function, and `qAD` computes the quantile function, of the null distribution of the Anderson-Darling test statistic.

### Usage

      pAD(q, n = Inf, lower.tail = TRUE, fast=TRUE)
      qAD(p, n = Inf, lower.tail = TRUE, fast=TRUE)

### Arguments

`q` | Numeric vector of quantiles (values for which the cumulative probability is required).
`p` | Numeric vector of probabilities.
`n` | Integer. Sample size for the Anderson-Darling test.
`lower.tail` | Logical. If `TRUE` (the default), probabilities are P(X <= q), and otherwise they are P(X > q).
`fast` | Logical value indicating whether to use a fast algorithm or a slower, more accurate algorithm, in the case `n=Inf`.

### Details

`pAD` uses the algorithms and C code described in Marsaglia and Marsaglia (2004).

`qAD` uses `uniroot` to find the quantiles.

The argument `fast` applies only when `n=Inf` and determines whether the asymptotic distribution is approximated using the faster algorithm `adinf` (accurate to 4-5 places) or the slower algorithm `ADinf` (accurate to 11 places) described in Marsaglia and Marsaglia (2004).

### Value

A numeric vector of the same length as `p` or `q`.

### Author(s)

Original C code by G. and J. 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.

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

### See Also

`ad.test`

### Examples

      pAD(1.1, n=5)
      pAD(1.1)
      pAD(1.1, fast=FALSE)

      qAD(0.5, n=5)
      qAD(0.5)

[Package goftest version 1.2-2 Index]