normal.test {energy} | R Documentation |
Performs the energy test of univariate normality for the composite hypothesis Case 4, estimated parameters.
normal.test(x, method=c("mc","limit"), R)
normal.e(x)
x |
univariate data vector |
method |
method for p-value |
R |
number of replications if Monte Carlo method |
If method="mc"
this test function applies the parametric
bootstrap method implemented in mvnorm.test
.
If method="limit"
, the p-value of the test is computed from
the asymptotic distribution of the test statistic under the null
hypothesis. The asymptotic
distribution is a quadratic form of centered Gaussian random variables,
which has the form
\sum_{k=1}^\infty \lambda_k Z_k^2,
where \lambda_k
are positive constants (eigenvalues) and
Z_k
are iid standard normal variables. Eigenvalues are
pre-computed and stored internally.
A p-value is computed using Imhof's method as implemented in the
CompQuadForm package.
Note that the "limit" method is intended for moderately large samples because it applies the asymptotic distribution.
The energy test of normality was proposed
and implemented by Szekely and Rizzo (2005).
See mvnorm.test
for more details.
normal.e
returns the energy goodness-of-fit statistic for
a univariate sample.
normal.test
returns a list with class htest
containing
statistic |
observed value of the test statistic |
p.value |
p-value of the test |
estimate |
sample estimates: mean, sd |
data.name |
description of data |
Maria L. Rizzo mrizzo@bgsu.edu and Gabor J. Szekely
Szekely, G. J. and Rizzo, M. L. (2005) A New Test for Multivariate Normality, Journal of Multivariate Analysis, 93/1, 58-80, doi: 10.1016/j.jmva.2003.12.002.
Mori, T. F., Szekely, G. J. and Rizzo, M. L. "On energy tests of normality." Journal of Statistical Planning and Inference 213 (2021): 1-15.
Rizzo, M. L. (2002). A New Rotation Invariant Goodness-of-Fit Test, Ph.D. dissertation, Bowling Green State University.
J. P. Imhof (1961). Computing the Distribution of Quadratic Forms in Normal Variables, Biometrika, Volume 48, Issue 3/4, 419-426.
mvnorm.test
and mvnorm.e
for the
energy test of multivariate normality and the test statistic
for multivariate samples.
x <- iris[1:50, 1]
normal.e(x)
normal.test(x, R=199)
normal.test(x, method="limit")