dpoisbinom function

The Poisson Binomial Distribution

Density, distribution function, quantile function and random generation for the Poisson binomial distribution with parameters size and prob.

This is conventionally interpreted as the number of successes in size * length(prob) trials with success probabilities prob.

dpoisbinom(x, size = 1, prob, log = FALSE)

ppoisbinom(q, size = 1, prob, lower.tail = TRUE, log.p = FALSE)

qpoisbinom(p, size = 1, prob, lower.tail = TRUE, log.p = FALSE)

rpoisbinom(n, size = 1, prob)

Arguments

• x, q: Vector of quantiles.
• size: The Poisson binomial distribution has size times the vector of probabilities prob.
• prob: Vector with the probabilities 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, $P(X > x)$.
• p: Vector of probabilities.
• n: Number of observations.

Returns

dpoisbinom gives the density, ppoisbinom gives the distribution function, qpoisbinom gives the quantile function and rpoisbinom generates random deviates.

The length of the result is determined by x, q, p

or n.

Details

The Poisson binomial distribution with size = 1 and prob $= (p_1,p_2,\ldots,p_n)$ has density

for $x=0,1,\ldots,n$; where $F_x$ is the set of all subsets of $x$ integers that can be selected from $\{1,2,\ldots,n\}$.

$p(x)$ is computed using Hong (2013) algorithm, see the reference below.

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

References

Hong Y (2013). “On Computing the Distribution Function for the Poisson Binomial Distribution.” Computational Statistics & Data Analysis, 59 (1), 41-51. tools:::Rd_expr_doi("10.1016/j.csda.2012.10.006") .

Author(s)

Jorge Castillo-Mateo