dcobin: Density function of cobin (continuous binomial) distribution

In cobin: Cobin and Micobin Regression Models for Continuous Proportional Data

Density function of cobin (continuous binomial) distribution

Description

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.

Usage

dcobin(x, theta, lambda, log = FALSE)

Arguments

x	num (length n), between 0 and 1, evaluation point
theta	scalar or length n vector, num (length 1 or n), natural parameter
lambda	scalar or length n vector, integer, inverse of dispersion parameter
log	logical (Default FALSE), if TRUE, return log density

Details

For the evaluation of h(y;\lambda), see ?cobin::dIH.

Value

density of cobin(\theta,\lambda^{-1})

Examples

xgrid = seq(0, 1, length = 500)
plot(xgrid, dcobin(xgrid, 0, 1), type="l", ylim = c(0,3)) # uniform 
lines(xgrid, dcobin(xgrid, 0, 3))
plot(xgrid, dcobin(xgrid, 2, 3), type="l")
lines(xgrid, dcobin(xgrid, -2, 3))

cobin documentation built on Sept. 2, 2025, 1:08 a.m.