| Posnegbin {VGAM} | R Documentation |
Density, distribution function, quantile function and random generation for the positive-negative binomial distribution.
dposnegbin(x, size, prob=NULL, munb=NULL, log=FALSE) pposnegbin(q, size, prob=NULL, munb=NULL) qposnegbin(p, size, prob=NULL, munb=NULL) rposnegbin(n, size, prob=NULL, munb=NULL)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of random values to return.
|
size, prob, munb, log |
Same arguments as that of an ordinary negative binomial distribution
(see dnbinom).
Some arguments have been renamed slightly.
Short vectors are recycled. The parameter 1/size is known as a dispersion parameter;
as size approaches infinity, the negative binomial distribution
approaches a Poisson distribution.
|
The positive-negative binomial distribution is a negative binomial distribution but with the probability of a zero being zero. The other probabilities are scaled to add to unity. The mean therefore is
munb / (1-p(0))
where munb the mean of an ordinary negative binomial distribution.
The arguments of
rposnegbin()
are fed into
rnbinom until n positive values
are obtained.
dposnegbin gives the density,
pposnegbin gives the distribution function,
qposnegbin gives the quantile function, and
rposnegbin generates n random deviates.
The running time
of rposnegbin()
is slow when munb is very close to zero.
T. W. Yee
Welsh, A. H., Cunningham, R. B., Donnelly, C. F. and Lindenmayer, D. B. (1996) Modelling the abundances of rare species: statistical models for counts with extra zeros. Ecological Modelling, 88, 297–308.
posnegbinomial,
rnbinom,
zanegbinomial.
munb = 5; size = 4; n = 1000
table(y <- rposnegbin(n, munb=munb, size=size))
mean(y) # sample mean
munb / (1 - (size/(size+munb))^size) # population mean
munb / pnbinom(0, mu=munb, size=size, lower.tail=FALSE) # same as before
x <- (-1):17
(ii = dposnegbin(x, munb=munb, size=size))
max(abs(cumsum(ii) - pposnegbin(x, munb=munb, size=size))) # Should be 0
## Not run:
x = 0:10
barplot(rbind(dposnegbin(x, munb=munb, size=size), dnbinom(x, mu=munb, size=size)),
beside = TRUE, col = c("blue","green"),
main=paste("dposnegbin(munb=", munb, ", size=", size, ") (blue) vs",
" dnbinom(mu=", munb, ", size=", size, ") (green)", sep=""),
names.arg = as.character(x))
## End(Not run)
# Another test for pposnegbin()
nn = 5000
mytab = cumsum(table(rposnegbin(nn, munb=munb, size=size))) / nn
myans = pposnegbin(sort(as.numeric(names(mytab))), munb=munb, size=size)
max(abs(mytab - myans)) # Should be 0