cobin (version 1.0.1.3)

pmicobin: 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)

Value

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

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.

Examples

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