The Poisson Distribution

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.

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.

Details

The Poisson distribution has density

p(x) = lambda^x exp(-lambda)/x!

for x = 0, 1, 2, ....

If an element of x is not integer, the result of dpois is zero, with a warning.

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")

-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")

[Package Contents]