R: Classical Goodness-of-Fit Tests

goftest-package {goftest} | R Documentation

## Classical Goodness-of-Fit Tests

### Description

Cramer-von Mises and Anderson-Darling tests of goodness-of-fit for continuous univariate distributions, using modern algorithms to compute the null distributions.

### Details

The goftest package contains implementations of the classical Cramer-von Mises and Anderson-Darling tests of goodness-of-fit for continuous univariate distributions.

The Cramer-von Mises test is performed by `cvm.test`. The cumulative distribution function of the null distribution of the test statistic is computed by `pCvM` using the algorithm of Csorgo and Faraway (1996). The quantiles are computed by `qCvM` by root-finding.

The Anderson-Darling test is performed by `ad.test`. The cumulative distribution function of the null distribution of the test statistic is computed by `pAD` using the algorithm of Marsaglia and Marsaglia (2004). The quantiles are computed by `qAD` by root-finding.

By default, each test assumes that the parameters of the null distribution are known (a simple null hypothesis). If the parameters were estimated (calculated from the data) then the user should set `estimated=TRUE` which uses the method of Braun (1980) to adjust for the effect of estimating the parameters from the data.

### Author(s)

Adrian Baddeley, Julian Faraway, John Marsaglia, George Marsaglia.

Maintainer: Adrian Baddeley <adrian.baddeley@uwa.edu.au>

### References

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.

Csorgo, S. and Faraway, J.J. (1996) The exact and asymptotic distributions of Cramer-von Mises statistics. Journal of the Royal Statistical Society, Series B 58, 221–234.

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

`ks.test`

### Examples

      x <- rnorm(30, mean=2, sd=1)
      # default behaviour: parameters fixed: simple null hypothesis
      cvm.test(x, "pnorm", mean=2, sd=1)
      ad.test(x, "pnorm", mean=2, sd=1)
      # parameters estimated: composite null hypothesis
      mu <- mean(x)
      sigma <- sd(x)
      cvm.test(x, "pnorm", mean=mu, sd=sigma, estimated=TRUE)
      ad.test(x, "pnorm", mean=mu, sd=sigma, estimated=TRUE)

[Package goftest version 1.2-2 Index]