pcobin: Cumulative distribution function of cobin (continuous...

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

Cumulative distribution 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

pcobin(q, theta, lambda)

Arguments

q	num (length n), between 0 and 1, evaluation point
theta	scalar, natural parameter
lambda	integer, inverse of dispersion parameter

Value

c.d.f. of cobin(\theta,\lambda^{-1})

Examples

xgrid = seq(0, 1, length = 500)
out = pcobin(xgrid, 1, 2)
plot(ecdf(rcobin(10000, 1, 2)))
lines(xgrid, out, col = 2)

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