| Poisson {base} | R Documentation |
The Poisson Distribution
Description
These functions provide information about the Poisson distribution
with parameter lambda. dpois gives the density,
ppois gives the distribution function qpois gives the
quantile function and rpois generates random deviates.
Usage
dpois(x, lambda)
ppois(q, lambda)
qpois(p, lambda)
rpois(n, lambda)
Arguments
x |
vector of (non-negative integer) quantiles. |
q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of random values to return. |
lambda |
vector of positive means. |
Details
The Poisson distribution has density
p(x) = \frac{{\lambda}^{x} {e}^{-\lambda}}{x!}
for x = 0, 1, 2, \ldots.
If an element of x is not integer, the result of dpois is zero,
with a warning.
The quantile is left continuous: qpois(q, lambda) is the largest
integer x such that P(X <= x) < q.
See Also
dbinom for the binomial and dnbinom for
the negative binomial distribution.
Examples
-log(dpois(0:7, lambda=1) * gamma(1+ 0:7))
Ni <- rpois(50, lam= 4); table(factor(Ni, 0:max(Ni)))
par(mfrow = c(2, 1))
x <- seq(-0.01, 5, 0.01)
plot(x, ppois(x, 1), type="s", ylab="F(x)", main="Poisson(1) CDF")
plot(x, pbinom(x, 100, 0.01),type="s", ylab="F(x)",
main="Binomial(100, 0.01) CDF")