frosini.norm.test: Frosini test for normality
In normtest: Tests for Normality

Description Usage Arguments Details Value Author(s) References Examples

Performs Frosini test for the composite hypothesis of normality, see e.g. Frosini (1987).

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

`x`	a numeric vector of data values.

nrepl

the number of replications in Monte Carlo simulation.

The Frosini test for normality is based on the following statistic:

B_n = \frac{1}{√{n}}∑_{i=1}^n{≤ft|Φ(Y_i) - \frac{i-0.5}{n} \right|},

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

Ilya Gavrilov and Ruslan Pusev

Frosini, B.V. (1987): On the distribution and power of a goodness-of-fit statistic with parametric and nonparametric applications, "Goodness-of-fit". (Ed. by Revesz P., Sarkadi K., Sen P.K.) — Amsterdam-Oxford-New York: North-Holland. — Pp. 133–154.

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

	Frosini test for normality

data:  rnorm(100)
B = 0.21138, p-value = 0.28


	Frosini test for normality

data:  runif(100, -1, 1)
B = 0.37774, p-value = 0.003