beta_inc

beta_inc_inv

Computes the incomplete beta function
$$I_x(a,b):=\int_0^x u^{a-1}(1-u)^{b-1}\,d\mathrm{u},\quad a,b&gt;0$$
and its inverse function.

internal

Implementation of uniformity tests on the circle and
(hyper)sphere. The main function of the package is unif_test(), which
conveniently collects more than 35 tests for assessing uniformity on
S^{p-1} = {x in R^p : ||x|| = 1}, p >= 2. The test statistics are
implemented in the unif_stat() function, which allows computing several
statistics for different samples within a single call, thus facilitating
Monte Carlo experiments. Furthermore, the unif_stat_MC() function allows
parallelizing them in a simple way. The asymptotic null distributions of
the statistics are available through the function unif_stat_distr(). The
core of 'sphunif' is coded in C++ by relying on the 'Rcpp' package.
The package also provides several novel datasets and gives the replicability
for the data applications/simulations in García-Portugués et al. (2021)
<doi:10.1007/978-3-030-69944-4_12>, García-Portugués et al. (2023)
<doi:10.3150/21-BEJ1454>, Fernández-de-Marcos and
García-Portugués (2024) <doi:10.1016/j.spl.2024.110218>, and
García-Portugués et al. (2025) <doi:10.1080/01621459.2025.2566414>.

Eduardo Portugues

sphunif

Uniformity Tests on the Circle, Sphere, and Hypersphere

Eduardo García-Portugués

Thomas Verdebout

Alberto Fernández-de-Marcos

Paula Navarro

beta_inc function

<dl><dt>x</dt>
<dd>a vector of size <code>nx</code> or a matrix of size <code>c(nx, 1)</code>.</dd>
<dt>a, b</dt>
<dd>scalars giving the parameters of the beta function.</dd>
<dt>lower_tail</dt>
<dd>accumulate the probability from the lower tail? If
<code>FALSE</code>, the probability is accumulated from the upper tail.
Defaults to <code>FALSE</code>.</dd>
<dt>log</dt>
<dd>use log-scale? If <code>TRUE</code>, returns the logarithm of the
incomplete beta function and uses log-scale for <code>u</code> in <code>beta_inc</code>.
Defaults to <code>FALSE</code>.</dd>
<dt>u</dt>
<dd>a vector of probabilities of size <code>nu</code> or a matrix of size
<code>c(nu, 1)</code>.</dd></dl>

Arguments

The incomplete beta function and its inverse — beta_inc

<dl>

<dt>x</dt>
<dd>a vector of size <code>nx</code> or a matrix of size <code>c(nx, 1)</code>.</dd>


<dt>a, b</dt>
<dd>scalars giving the parameters of the beta function.</dd>


<dt>lower_tail</dt>
<dd>accumulate the probability from the lower tail? If
<code>FALSE</code>, the probability is accumulated from the upper tail.
Defaults to <code>FALSE</code>.</dd>


<dt>log</dt>
<dd>use log-scale? If <code>TRUE</code>, returns the logarithm of the
incomplete beta function and uses log-scale for <code>u</code> in <code>beta_inc</code>.
Defaults to <code>FALSE</code>.</dd>


<dt>u</dt>
<dd>a vector of probabilities of size <code>nu</code> or a matrix of size
<code>c(nu, 1)</code>.</dd>

</dl>

beta_inc: The incomplete beta function and its inverse

Description

Usage

Value

Arguments

Details