lawstat (version 3.2)

rlm.test: Robust L1 Moment-Based (RLM) Goodness-of-Fit Test for the Laplace Distribution

Description

This function performs the robust test for the Laplace distribution. Two options for calculating critical values, namely, approximated with chisq distribution and empirical, are available.

Usage

rlm.test(x, crit.values = c("chisq.approximation", "empirical"), N = 0)

Arguments

x

a numeric vector of data values.

crit.values

a character string specifying how the critical values should be obtained, i.e., approximated by the chisq-distribution (default) or empirical.

N

number of Monte Carlo simulations for the empirical critical values

Value

A list with class htest containing the following components:

statistic

the value of the test statistic.

parameter

the degrees of freedom.

p.value

the p-value of the test.

method

type of test was performed.

data.name

a character string giving the name of the data.

Details

The test is based on a joint statistic using skewness and kurtosis coefficients. In particular, RLM uses the Average Absolute Deviation from the Median (MAAD), a robust estimate of standard deviation.

References

Gastwirth, J. L.(1982) Statistical Properties of A Measure of Tax Assessment Uniformity, Journal of Statistical Planning and Inference 6, 1-12.

Gel, Y. R. (2009) Test of fit for a Laplace distribution against heavier tailed alternatives, Working paper.

See Also

sj.test, rjb.test, rqq, jarque.bera.test (in tseries package).

Examples

# NOT RUN {
## Laplace distributed data
x = rexp(100)-rexp(100)
rlm.test(x)

## Sample Output
##
##        Robust L1 moment-based goodness-of-fit test using a Chi-squared approximated 
##        critical values
##
## data:  x
## Chi-squared statistic = 0.3945, df = 2, p-value = 0.821

# }