Pospois {VGAM} | R Documentation |
Density, distribution function, quantile function and random generation for the positive-Poisson distribution.
dpospois(x, lambda, log = FALSE) ppospois(q, lambda) qpospois(p, lambda) rpospois(n, lambda)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations.
Fed into |
lambda |
vector of positive means (of an ordinary Poisson distribution). Short vectors are recycled. |
log |
logical. |
The positive-Poisson distribution is a Poisson distribution but with the probability of a zero being zero. The other probabilities are scaled to add to unity. The mean therefore is
lambda / (1-exp(-lambda)).
As lambda increases, the positive-Poisson and Poisson
distributions become more similar.
Unlike similar functions for the Poisson distribution, a zero value
of lambda
is not permitted here.
dpospois
gives the density,
ppospois
gives the distribution function,
qpospois
gives the quantile function, and
rpospois
generates random deviates.
The family function pospoisson
estimates
lambda by maximum likelihood estimation.
T. W. Yee
pospoisson
,
zapoisson
,
zipoisson
,
rpois
.
lambda <- 2; y = rpospois(n = 1000, lambda) table(y) mean(y) # Sample mean lambda / (1 - exp(-lambda)) # Population mean (ii <- dpospois(0:7, lambda)) cumsum(ii) - ppospois(0:7, lambda) # Should be 0s table(rpospois(100, lambda)) table(qpospois(runif(1000), lambda)) round(dpospois(1:10, lambda) * 1000) # Should be similar ## Not run: x <- 0:7 barplot(rbind(dpospois(x, lambda), dpois(x, lambda)), beside = TRUE, col = c("blue", "orange"), main = paste("Positive Poisson(", lambda, ") (blue) vs", " Poisson(", lambda, ") (orange)", sep = ""), names.arg = as.character(x), las = 1, lwd = 2) ## End(Not run)