dmicobin

Micobin distribution with natural parameter $\theta$ and dispersion $psi$, denoted as $micobin(\theta, \psi)$, is defined as a dispersion mixture of cobin:
$$
 Y \sim micobin(\theta, \psi) \iff Y | \lambda \sim cobin(\theta, \lambda^{-1}), (\lambda-1) \sim negbin(2, \psi) 
$$
so that micobin density is a weighted sum of cobin density with negative binomial weights.

Provides functions for cobin and micobin regression models, a new family of generalized linear models for continuous proportional data (Y in the closed unit interval [0, 1]). It also includes an exact, efficient sampler for the Kolmogorov-Gamma random variable. For details, see Lee et al. (2025+) <doi:10.48550/arXiv.2504.15269>.

Changwoo Lee

cobin

Cobin and Micobin Regression Models for Continuous Proportional
Data

Benjamin Dahl

Otso Ovaskainen

David Dunson

dmicobin function

<dl><dt>x</dt>
<dd>num (length n), between 0 and 1, evaluation point</dd>
<dt>theta</dt>
<dd>scalar or length n vector, natural parameter</dd>
<dt>psi</dt>
<dd>scalar or length n vector, between 0 and 1, dispersion parameter</dd>
<dt>r</dt>
<dd>(Default 2) This should be always 2 to maintain interpretaton of psi. It is kept for future experiment purposes.</dd>
<dt>log</dt>
<dd>logical (Default FALSE), if TRUE, return log density</dd>
<dt>l_max</dt>
<dd>integer (Default 70), upper bound of lambda.</dd></dl>

Arguments

Density function of micobin (mixture of continuous binomial) distribution — dmicobin

<dl>

<dt>x</dt>
<dd>num (length n), between 0 and 1, evaluation point</dd>


<dt>theta</dt>
<dd>scalar or length n vector, natural parameter</dd>


<dt>psi</dt>
<dd>scalar or length n vector, between 0 and 1, dispersion parameter</dd>


<dt>r</dt>
<dd>(Default 2) This should be always 2 to maintain interpretaton of psi. It is kept for future experiment purposes.</dd>


<dt>log</dt>
<dd>logical (Default FALSE), if TRUE, return log density</dd>


<dt>l_max</dt>
<dd>integer (Default 70), upper bound of lambda.</dd>

</dl>

dmicobin: Density function of micobin (mixture of continuous binomial) distribution

Description

Usage

Value

Arguments

Examples