Irwin-Hall distribution is defined as a sum of m uniform (0,1) distribution.
Its density is given as
$$
 f(x;m) = \frac{1}{(m-1)!}\sum_{k=0}^{m} (-1)^k {m \choose k} \max(0,x-k)^{m-1}, 0 &lt; x &lt; m
$$
The density of Bates distribution, defined as an average of m uniform (0,1) distribution, can be obtained from change-of-variable (y = x/m),
$$
 h(y;m) = \frac{m}{(m-1)!}\sum_{k=0}^{m} (-1)^k {m \choose k} \max(0,my-k)^{m-1}, 0 &lt; y &lt; 1
$$

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

dIH function

<dl><dt>x</dt>
<dd>vector of quantities, between 0 and m</dd>
<dt>m</dt>
<dd>integer, parameter</dd>
<dt>log</dt>
<dd>logical, return log density if TRUE</dd></dl>

Arguments

Density of Irwin-Hall distribution — dIH

<dl>

<dt>x</dt>
<dd>vector of quantities, between 0 and m</dd>


<dt>m</dt>
<dd>integer, parameter</dd>


<dt>log</dt>
<dd>logical, return log density if TRUE</dd>

</dl>

dIH: Density of Irwin-Hall distribution

Description

Usage

Value

Arguments

Details

Examples