ajb.norm.test: Adjusted Jarque-Bera test for normality
In normtest: Tests for Normality

Description Usage Arguments Details Value Author(s) References Examples

Performs adjusted Jarque–Bera test for the composite hypothesis of normality, see Urzua (1996).

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

`x`	a numeric vector of data values.

nrepl

the number of replications in Monte Carlo simulation.

The adjusted Jarque–Bera test for normality is based on the following statistic:

AJB = \frac{(√{b_1})^2}{\mathrm{Var}≤ft(√{b_1}\right)} + \frac{(b_2 - \mathrm{E}≤ft(b_2\right))^2}{\mathrm{Var}≤ft(b_2\right)},

where

√{b_1} = \frac{\frac{1}{n}∑_{i=1}^n(X_i - \overline{X})^3}{≤ft(\frac{1}{n}∑_{i=1}^n(X_i - \overline{X})^2\right)^{3/2}}, \quad b_2 = \frac{\frac{1}{n}∑_{i=1}^n(X_i - \overline{X})^4}{≤ft(\frac{1}{n}∑_{i=1}^n(X_i - \overline{X})^2\right)^2},

\mathrm{Var}≤ft(√{b_1}\right) = \frac{6(n-2)}{(n+1)(n+3)}, \quad E≤ft(b_2\right) = \frac{3(n-1)}{n+1}, \quad \mathrm{Var}≤ft(b_2\right) = \frac{24n(n-2)(n-3)}{(n+1)^2(n+3)(n+5)}.

The p-value is computed by Monte Carlo simulation.

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

`statistic`	the value of the adjusted Jarque–Bera statistic.
`p.value`	the p-value for the test.
`method`	the character string "Adjusted Jarque-Bera test for normality".
`data.name`	a character string giving the name(s) of the data.

Ilya Gavrilov and Ruslan Pusev

Urzua, C. M. (1996): On the correct use of omnibus tests for normality. — Economics Letters, vol. 53, pp. 247–251.

1 2	ajb.norm.test(rnorm(100)) ajb.norm.test(abs(runif(100,-2,5)))

	Adjusted Jarque-Bera test for normality

data:  rnorm(100)
AJB = 0.51703, p-value = 0.7565


	Adjusted Jarque-Bera test for normality

data:  abs(runif(100, -2, 5))
AJB = 7.2093, p-value = 0.0415