spiegelhalter.norm.test: Spiegelhalter test for normality

Description Usage Arguments Details Value Author(s) References Examples

Description

Performs Spiegelhalter test for the composite hypothesis of normality, see Spiegelhalter (1977).

Usage

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

Arguments

x

a numeric vector of data values.

nrepl

the number of replications in Monte Carlo simulation.

Details

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

T = ≤ft( (c_nu)^{-(n-1)}+g^{-(n-1)} \right)^{1/(n-1)},

where

u=\frac{X_{(n)}-X_{(1)}}{s}, \quad g=\frac{∑_{i=1}^n|X_i-\overline{X}|}{s√{n(n-1)}}, \quad c_n=\frac{(n!)^{1/(n-1)}}{2n}, \quad s^2=\frac{1}{n-1}∑_{i=1}^n(X_i-\overline{X})^2.

The p-value is computed by Monte Carlo simulation.

Value

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

statistic

the value of the Geary statistic.

p.value

the p-value for the test.

method

the character string "Spiegelhalter test for normality".

data.name

a character string giving the name(s) of the data.

Author(s)

Ilya Gavrilov and Ruslan Pusev

References

Spiegelhalter, D. J. (1977): A test for normality against symmetric alternatives. — Biometrika, vol. 64, pp. 415–418.

Examples

1
2

Example output

	Spiegelhalter test for normality

data:  rnorm(100)
T = 1.2648, p-value = 0.324


	Spiegelhalter test for normality

data:  rexp(100)
T = 1.6349, p-value < 2.2e-16

normtest documentation built on May 2, 2019, 7:28 a.m.