Positive-Geometric Distribution
Density, distribution function, quantile function and random generation for the positive-geometric distribution.
dposgeom(x, prob, log = FALSE) pposgeom(q, prob) qposgeom(p, prob) rposgeom(n, prob)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations.
Fed into |
prob |
vector of probabilities of success (of an ordinary geometric distribution). Short vectors are recycled. |
log |
logical. |
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.
dposgeom gives the density,
pposgeom gives the distribution function,
qposgeom gives the quantile function, and
rposgeom generates random deviates.
T. W. Yee
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)
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.