hegazy2.norm.test: Hegazy-Green test for normality
In normtest: Tests for Normality

Description Usage Arguments Details Value Author(s) References Examples

Performs Hegazy–Green test for the composite hypothesis of normality, see e.g. Hegazy and Green (1975).

1	hegazy2.norm.test(x, nrepl=2000)

`x`	a numeric vector of data values.

nrepl

the number of replications in Monte Carlo simulation.

The Hegazy–Green test for normality is based on the following statistic:

T_2 = \frac{1}{n}∑_{i=1}^n{≤ft(Y_{i}-Φ^{-1}{≤ft(\frac{i}{n+1}\right)}\right)^2}.

where

Y_i=\frac{X_{(i)}-\overline{X}}{s}, \quad s^2=\frac{1}{n}∑_{i=1}^n(X_i-\overline{X})^2.

The p-value is computed by Monte Carlo simulation.

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

`statistic`	the value of the Hegazy–Green statistic.
`p.value`	the p-value for the test.
`method`	the character string "Hegazy-Green test for normality".
`data.name`	a character string giving the name(s) of the data.

Gavrilov Ilya and Ruslan Pusev

Hegazy, Y. A. S. and Green, J. R. (1975): Some new goodness-of-fit tests using order statistics. — Journal of the Royal Statistical Society. Series C (Applied Statistics), vol. 24, pp. 299–308.

1 2	hegazy2.norm.test(rnorm(100)) hegazy2.norm.test(runif(100,-1,1))

	Hegazy-Green test for normality

data:  rnorm(100)
T = 0.009465, p-value = 0.711


	Hegazy-Green test for normality

data:  runif(100, -1, 1)
T = 0.039243, p-value = 0.008