Positive-Binomial Distribution
Density, distribution function, quantile function and random generation for the positive-binomial distribution.
dposbinom(x, size, prob, log = FALSE) pposbinom(q, size, prob) qposbinom(p, size, prob) rposbinom(n, size, prob)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations.
Fed into |
size |
number of trials.
It is the N symbol in the formula
given in |
prob |
probability of success on each trial. Should be in (0,1). |
log |
See
|
The positive-binomial distribution is a binomial distribution but with the probability of a zero being zero. The other probabilities are scaled to add to unity. The mean therefore is
mu / (1-(1-mu)^N)
where mu is the argument prob above.
As mu increases, the positive-binomial and binomial
distributions become more similar.
Unlike similar functions for the binomial distribution, a zero value
of prob is not permitted here.
dposbinom gives the density,
pposbinom gives the distribution function,
qposbinom gives the quantile function, and
rposbinom generates random deviates.
These functions are or are likely to be deprecated.
Use Gaitbinom instead.
For dposbinom(), if arguments size or prob
equal 0 then a NaN is returned.
The family function posbinomial estimates the
parameters by maximum likelihood estimation.
T. W. Yee.
prob <- 0.2; size <- 10
table(y <- rposbinom(n = 1000, size, prob))
mean(y) # Sample mean
size * prob / (1 - (1 - prob)^size) # Population mean
(ii <- dposbinom(0:size, size, prob))
cumsum(ii) - pposbinom(0:size, size, prob) # Should be 0s
table(rposbinom(100, size, prob))
table(qposbinom(runif(1000), size, prob))
round(dposbinom(1:10, size, prob) * 1000) # Should be similar
## Not run: barplot(rbind(dposbinom(x = 0:size, size, prob),
dbinom(x = 0:size, size, prob)),
beside = TRUE, col = c("blue", "green"),
main = paste("Positive-binomial(", size, ",",
prob, ") (blue) vs",
" Binomial(", size, ",", prob, ") (green)", sep = ""),
names.arg = as.character(0:size), las = 1)
## End(Not run)
# Simulated data example
nn <- 1000; sizeval1 <- 10; sizeval2 <- 20
pdata <- data.frame(x2 = seq(0, 1, length = nn))
pdata <- transform(pdata, prob1 = logitlink(-2 + 2 * x2, inverse = TRUE),
prob2 = logitlink(-1 + 1 * x2, inverse = TRUE),
sizev1 = rep(sizeval1, len = nn),
sizev2 = rep(sizeval2, len = nn))
pdata <- transform(pdata, y1 = rposbinom(nn, size = sizev1, prob = prob1),
y2 = rposbinom(nn, size = sizev2, prob = prob2))
with(pdata, table(y1))
with(pdata, table(y2))
# Multiple responses
fit2 <- vglm(cbind(y1, y2) ~ x2, posbinomial(multiple.responses = TRUE),
trace = TRUE, data = pdata, weight = cbind(sizev1, sizev2))
coef(fit2, matrix = TRUE)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.