qualityTools (version 1.55)

adSim: Bootstrap-based Anderson-Darling Test for Univariate Distributions

Description

Anderson-Darling test for univariate distributions with bootstrap-based p-value determination. It also enables the p-value determination from tabled critical values.

Usage

adSim(x, distribution = "normal", b = 10000)

Arguments

x

A numeric vector.

distribution

A character string. Distributions "cauchy", "exponential", "gumbel", "gamma", "log-normal", "lognormal", "logistic", "normal" and "weibull" are recognized.

b

A numeric value giving the frequency of bootstraps. Any value in [1000,1000000] is allowed. If b is set to NA, the Anderson-Darling test will be applied without simulation. b should be chosen carefully. High values such as 1 mio can easily make your computer run up to 3 hours (depending on the distribution, on the sample size and on your computer system).

Value

An object of class "adSim", a list with six components,

distribution

the distribution the Anderson-Darling test was applied for

parameter_estimation

the estimated parameters

Anderson_Darling

the value of the Anderson-Darling test

p_value

the corresponding p-value (simulated or tabled value)

crititical_values

the corresponding critical values (simulated or tabled 0.75, 0.90, 0.95, 0.975 and 0.99 quantiles)

simAD

bootstrap-based Anderson-Darling distribution

Details

First parameter estimation for the tested distribution is performed. In the majority of cases Maximum-Likelihood-Estimation is used as fitting method and is mainly provided by fitdistr() from package MASS. Parameters of normal and log-normal distribution are fitted by mean and standard deviation. Cauchy parameters are fitted by the sums of the weighted order statistic, when p-value determination should be done from tabled critical values. The Anderson-Darling statistic is calculated based on the estimated parameters. Parametric bootstrapping provides the distribution of the Anderson-Darling test which is used in order to determine a p-value. Simulation-based Anderson-Darling distribution and critical values for selected quantiles are printable. When simulation is not desired, a p-value is obtained from tabled critical values (no exact expression exists except for log-normal, normal and exponential distribution). Tabled critical values for selected quantiles are printable as well.

References

Stute, W./ Manteiga, W./ Quindimil, M.(1993): Bootstrap based goodness-of-fit-tests; Metrika, Vol. 40, p.243-256; Physica Verlag D'Agostino, R.B./ Stephens, M.A. (1986): Goodness-Of-Fit Techniques; illustrated edition; p.97-193; Marcel Dekker Inc.

See Also

http://www.r-qualitytools.org

Examples

x <- rnorm(25,32,2)
adSim(x)
adSim(x,"logistic",2000)
adSim(x,"cauchy",NA)