VGAM (version 1.0-2)

Oiposbinom: One-Inflated Positive Binomial Distribution

Description

Density, distribution function, quantile function and random generation for the one-inflated positive binomial distribution with parameter pstr1.

Usage

doiposbinom(x, size, prob, pstr1 = 0, log = FALSE)
poiposbinom(q, size, prob, pstr1 = 0)
qoiposbinom(p, size, prob, pstr1 = 0)
roiposbinom(n, size, prob, pstr1 = 0)

Arguments

x, p, q, n

Same as Posbinom.

size, prob

Same as Posbinom.

pstr1

Probability of a structural one (i.e., ignoring the positive binomial distribution), called $phi$. The default value of $phi = 0$ corresponds to the response having a positive binomial distribution.

log

Logical. Return the logarithm of the answer?

Value

doiposbinom gives the density, poiposbinom gives the distribution function, qoiposbinom gives the quantile function, and roiposbinom generates random deviates.

Details

The probability function of $Y$ is 1 with probability $phi$, and $PosBinomial(size, prob)$ with probability $1-phi$. Thus $$P(Y=1) =\phi + (1-\phi) P(W=1)$$ where $W$ is distributed as a positive $binomial(size, prob)$ random variate.

See Also

posbinomial, dbinom, binomialff.

Examples

size <- 10; prob <- 0.2; pstr1 <- 0.4; x <- (-1):size
(ii <- doiposbinom(x, size, prob, pstr1 = pstr1))
table(roiposbinom(100, size, prob, pstr1 = pstr1))
round(doiposbinom(x  , size, prob, pstr1 = pstr1) * 100)  # Should be similar

## Not run:  x <- 0:size
# par(mfrow = c(2, 1))  # One-Inflated Positive Binomial
# barplot(rbind(doiposbinom(x, size, prob, pstr1 = pstr1),
#               dposbinom(x, size, prob)),
#         beside = TRUE, col = c("blue", "orange"),
#         main = paste("OIPB(", size, ",", prob, ", pstr1 = ", pstr1, ") (blue) vs",
#                      " PosBinomial(", size, ",", prob, ") (orange)", sep = ""),
#         names.arg = as.character(x))
# 
# # Zero-deflated Pos Binomial
# deflat.limit <- -dposbinom(1, size, prob) / (1 - dposbinom(1, size, prob))
# deflat.limit <- size * prob / (1 + (size-1) * prob - 1 / (1-prob)^(size-1))
# newpstr1 <- round(deflat.limit, 3) + 0.001  # A little from the boundary
# barplot(rbind(doiposbinom(x, size, prob, pstr1 = newpstr1),
#                 dposbinom(x, size, prob)),
#         beside = TRUE, col = c("blue","orange"),
#         main = paste("ODPB(", size, ",", prob, ", pstr1 = ", newpstr1, ") (blue) vs",
#                      " PosBinomial(", size, ",", prob, ") (orange)", sep = ""),
#         names.arg = as.character(x)) ## End(Not run)