VGAM (version 1.0-6)

Oapospois: One-Altered Logarithmic Distribution

Description

Density, distribution function, quantile function and random generation for the one-altered positive-Poisson distribution with parameter pobs1.

Usage

doapospois(x, lambda, pobs1 = 0, log = FALSE)
poapospois(q, lambda, pobs1 = 0)
qoapospois(p, lambda, pobs1 = 0)
roapospois(n, lambda, pobs1 = 0)

Arguments

x, q, n, p

Same Unif.

lambda, log

Same as Otpospois).

pobs1

Probability of (an observed) one, called \(pobs1\). The default value of pobs1 = 0 corresponds to the response having a 1-truncated positive-Poisson distribution.

Value

doapospois gives the density and poapospois gives the distribution function, qoapospois gives the quantile function, and roapospois generates random deviates.

Details

The probability function of \(Y\) is 1 with probability pobs1, else a 1-truncated positive-Poisson(lambda) distribution.

See Also

oapospoisson, Oipospois, Otpospois.

Examples

# NOT RUN {
lambda <- 3; pobs1 <- 0.30; x <- (-1):7
doapospois(x, lambda = lambda, pobs1 = pobs1)
table(roapospois(100, lambda = lambda, pobs1 = pobs1))

# }
# NOT RUN {
 x <- 0:10
barplot(rbind(doapospois(x, lambda = lambda, pobs1 = pobs1),
                dpospois(x, lambda = lambda)),
        beside = TRUE, col = c("blue", "orange"), cex.main = 0.7, las = 1,
        ylab = "Probability", names.arg = as.character(x),
        main = paste("OAPP(lambda = ", lambda, ", pobs1 = ", pobs1,
                   ") [blue] vs",  " PosPoisson(lambda = ", lambda,
                   ") [orange] densities", sep = "")) 
# }