VGAM (version 1.1-4)

Posgeom: Positive-Geometric Distribution

Description

Density, distribution function, quantile function and random generation for the positive-geometric distribution.

Usage

dposgeom(x, prob, log = FALSE)
pposgeom(q, prob)
qposgeom(p, prob)
rposgeom(n, prob)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. Fed into runif.

prob

vector of probabilities of success (of an ordinary geometric distribution). Short vectors are recycled.

log

logical.

Value

dposgeom gives the density, pposgeom gives the distribution function, qposgeom gives the quantile function, and rposgeom generates random deviates.

Details

The positive-geometric distribution is a geometric distribution but with the probability of a zero being zero. The other probabilities are scaled to add to unity. The mean therefore is \(1/prob\).

As \(prob\) decreases, the positive-geometric and geometric distributions become more similar. Like similar functions for the geometric distribution, a zero value of prob is not permitted here.

See Also

zageometric, zigeometric, rgeom.

Examples

# NOT RUN {
prob <- 0.75; y <- rposgeom(n = 1000, prob)
table(y)
mean(y)  # Sample mean
1 / prob  # Population mean

(ii <- dposgeom(0:7, prob))
cumsum(ii) - pposgeom(0:7, prob)  # Should be 0s
table(rposgeom(100, prob))

table(qposgeom(runif(1000), prob))
round(dposgeom(1:10, prob) * 1000)  # Should be similar

# }
# NOT RUN {
x <- 0:5
barplot(rbind(dposgeom(x, prob), dgeom(x, prob)),
        beside = TRUE, col = c("blue", "orange"),
        main = paste("Positive geometric(", prob, ") (blue) vs",
        " geometric(", prob, ") (orange)", sep = ""),
        names.arg = as.character(x), las = 1, lwd = 2) 
# }