---
title: "KEPTED"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{KEPTED}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup}
library(KEPTED)
```


This package provides an implementation of a kernel-embedding of probability test for elliptical distribution. This is a guide to perform the asymptotic test for elliptical distribution under general alternatives, and the location and shape parameters are assumed to be unknown. 

To conduct the test for elliptical distribution, we can directly use the EllKEPT function as follows.

```{r}
n=200
d=3

## test under a null distribution
X=matrix(rnorm(d*n),nrow=n,ncol=d)
EllKEPT(X,kerU="Gaussian",kerTheta="Gaussian")
EllKEPT(X,kerU="PIQ",kerTheta="PIQ")

## test under an alternative distribution
X=matrix(rchisq(d*n,2),nrow=n,ncol=d)
EllKEPT(X,kerU="Gaussian",kerTheta="Gaussian")
EllKEPT(X,kerU="PIQ",kerTheta="PIQ")
```