cvm.test {rotRPackage}R Documentation

Cramer-von Mises test for normality. Taken from the "nortest" package by Juergen Gross, available on CRAN

Description

Performs the Cramer-von Mises test for the composite hypothesis of normality, see e.g. Thode (2002, Sec. 5.1.3).

Usage

cvm.test(x)

Arguments

x a numeric vector of data values, the number of which must be greater than 7. Missing values are allowed.

Details

The Cramer-von Mises test is an EDF omnibus test for the composite hypothesis of normality. The test statistic is

W = frac{1}{12 n} + sum_{i=1}^{n} (p_{(i)} - frac{2i-1}{2n}),

where p_{(i)} = Phi([x_{(i)} - overline{x}]/s). Here, Phi is the cumulative distribution function of the standard normal distribution, and overline{x} and s are mean and standard deviation of the data values. The p-value is computed from the modified statistic Z=W (1.0 + 0.5/n) according to Table 4.9 in Stephens (1986).

Value

A list with class "htest" containing the following components:

statistic the value of the Cramer-von Mises statistic.
p.value the p-value for the test.
method the character string "Cramer-von Mises normality test".
data.name a character string giving the name(s) of the data.

Author(s)

Juergen Gross

References

Stephens, M.A. (1986): Tests based on EDF statistics. In: D'Agostino, R.B. and Stephens, M.A., eds.: Goodness-of-Fit Techniques. Marcel Dekker, New York.

Thode Jr., H.C. (2002): Testing for Normality. Marcel Dekker, New York.

Examples

cvm.test(rnorm(100, 5, 3))
cvm.test(rnorm(100, 2, 4))


[Package rotRPackage version 1.4.3 Index]