We generated \(n=200\) observations from the uniform distribution on \(S^{d-1}\), with \(d=3\), and \(\rho = 0.7\).

```
library(QuadratiK)
n <- 200
d <- 3
set.seed(2468)
z <- matrix(rnorm(n * d), n, d)
dat_sphere <- z/sqrt(rowSums(z^2))
```

The `pk.test`

is used for testing uniformity of the
generated sample.

```
##
## Poisson Kernel-based quadratic distance test of
## Uniformity on the Sphere
## Selected consentration parameter rho: 0.7
##
## U-statistic:
##
## H0 is rejected: FALSE
## Statistic Un: -0.9756673
## Critical value: 1.725683
##
## V-statistic:
##
## H0 is rejected: FALSE
## Statistic Vn: 14.89598
## Critical value: 23.22949
```

The `summary`

method for the `pk.test`

output
object provides the results of the performed test, and generates a
figure showing the qq-plots against the uniform distribution of each
variable with a table of standard descriptive statistics.

```
##
## Poisson Kernel-based quadratic distance test of
## Uniformity on the Sphere
## Test_Statistics Critical_Value Reject_H0
## 1 -0.9756673 1.725683 FALSE
## 2 14.8959834 23.229487 FALSE
```

The figure automatically generated by the `summary`

function on the result of the test for uniformity displays the qq-plots
between the given samples and the uniform distribution with a table of
the standard descriptive statistics for each variable.