Rlab (version 4.0)

Bernoulli: The Bernoulli Distribution

Description

Density, distribution function, quantile function and random generation for the Bernoulli distribution with parameter prob.

Usage

dbern(x, prob, log = FALSE)
pbern(q, prob, lower.tail = TRUE, log.p = FALSE)
qbern(p, prob, lower.tail = TRUE, log.p = FALSE)
rbern(n, prob)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

prob

probability of success on each trial.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).

Value

dbern gives the density, pbern gives the distribution function, qbern gives the quantile function and rbern generates random deviates.

Details

The Bernoulli distribution with prob \(= p\) has density $$p(x) = {p}^{x} {(1-p)}^{1-x}$$ for \(x = 0 or 1\).

If an element of x is not 0 or 1, the result of dbern is zero, without a warning. \(p(x)\) is computed using Loader's algorithm, see the reference below.

The quantile is defined as the smallest value \(x\) such that \(F(x) \ge p\), where \(F\) is the distribution function.

References

Catherine Loader (2000). Fast and Accurate Computation of Binomial Probabilities; manuscript available from http://cm.bell-labs.com/cm/ms/departments/sia/catherine/dbinom

See Also

dbinom for the binomial (Bernoulli is a special case of the binomial), and dpois for the Poisson distribution.

Examples

# NOT RUN {
# Compute P(X=1) for X Bernoulli(0.7)
dbern(1, 0.7)
# }