pmicobin: Cumulative distribution function of micobin (mixture of...

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

Cumulative distribution 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 cdf is a weighted sum of cobin cdf with negative binomial weights.

Usage

pmicobin(q, theta, psi, r = 2, l_max = 70)

Arguments

q	num (length n), between 0 and 1, evaluation point
theta	scalar, natural parameter
psi	scalar, dispersion parameter
r	(Default 2) This should be always 2 to maintain interpretaton of psi. It is kept for future experiment purposes.
l_max	integer (Default 70), upper bound of lambda.

Value

c.d.f. of micobin(\theta, \psi)

Examples

xgrid = seq(0, 1, length = 500)
out = pmicobin(xgrid, 1, 1/2)
plot(ecdf(rmicobin(10000, 1, 1/2)))
lines(xgrid, out, col = 2)

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