dcobin

Continuous binomial distribution with natural parameter $\theta$ and dispersion parameter $1/\lambda$, in short $Y \sim cobin(\theta, \lambda^{-1})$, has density
$$
 p(y; \theta, \lambda^{-1}) = h(y;\lambda) \exp(\lambda \theta y - \lambda B(\theta)), \quad 0 \le y \le 1
$$
where $B(\theta) = \log\{(e^\theta - 1)/\theta\}$ and $h(y;\lambda) = \frac{\lambda}{(\lambda-1)!}\sum_{k=0}^{\lambda} (-1)^k {\lambda \choose k} \max(0,\lambda y-k)^{\lambda-1}$.
When $\lambda = 1$, it becomes continuous Bernoulli distribution.

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

dcobin 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, num (length 1 or n), natural parameter</dd>
<dt>lambda</dt>
<dd>scalar or length n vector, integer, inverse of dispersion parameter</dd>
<dt>log</dt>
<dd>logical (Default FALSE), if TRUE, return log density</dd></dl>

Arguments

Density function of cobin (continuous binomial) distribution — dcobin

<dl>

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


<dt>theta</dt>
<dd>scalar or length n vector, num (length 1 or n), natural parameter</dd>


<dt>lambda</dt>
<dd>scalar or length n vector, integer, inverse of dispersion parameter</dd>


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

</dl>

dcobin: Density function of cobin (continuous binomial) distribution

Description

Usage

Value

Arguments

Details

Examples