rcobin: Random variate generation for cobin (continuous binomial)...

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

Random variate generation for 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

rcobin(n, theta, lambda)

Arguments

n	integer, number of samples
theta	scalar or length n vector, natural parameter.
lambda	scalar or length n vector, inverse of dispersion parameter. Must be integer, length should be same as theta

Details

The random variate generation is based on the fact that cobin(\theta, \lambda^{-1}) is equal in distribution to the sum of \lambda cobin(\theta, 1) random variables, scaled by \lambda^{-1}. Random variate generation for continuous Bernoulli is done by inverse cdf transform method.

Value

random samples from cobin(\theta,\lambda^{-1}).

Examples

hist(rcobin(1000, 2, 3), freq = FALSE)
xgrid = seq(0, 1, length = 500)
lines(xgrid, dcobin(xgrid, 2, 3))

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