dmicobin: Density function of micobin (mixture of continuous binomial)...

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

Density function of micobin (mixture of continuous binomial) distribution

Description

Micobin distribution with natural parameter \theta and dispersion psi, denoted as micobin(\theta, \psi), is defined as a dispersion mixture of cobin:

Y \sim micobin(\theta, \psi) \iff Y | \lambda \sim cobin(\theta, \lambda^{-1}), (\lambda-1) \sim negbin(2, \psi)

so that micobin density is a weighted sum of cobin density with negative binomial weights.

Usage

dmicobin(x, theta, psi, r = 2, log = FALSE, l_max = 70)

Arguments

x	num (length n), between 0 and 1, evaluation point
theta	scalar or length n vector, natural parameter
psi	scalar or length n vector, between 0 and 1, dispersion parameter
r	(Default 2) This should be always 2 to maintain interpretaton of psi. It is kept for future experiment purposes.
log	logical (Default FALSE), if TRUE, return log density
l_max	integer (Default 70), upper bound of lambda.

Value

density of micobin(\theta, \psi)

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.