Poisson-Binomial | R Documentation |
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)
x, q |
Vector of quantiles. |
size |
The Poisson binomial distribution has |
prob |
Vector with the probabilities of success on each trial. |
log, log.p |
Logical. If |
lower.tail |
Logical. If |
p |
Vector of probabilities. |
n |
Number of observations. |
The Poisson binomial distribution with size = 1
and
prob
= (p_1,p_2,\ldots,p_n)
has density
p(x) = \sum_{A \in F_x} \prod_{i \in A} p_i \prod_{j \in A^c} (1-p_j)
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.
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
.
Jorge Castillo-Mateo
Hong Y (2013). “On Computing the Distribution Function for the Poisson Binomial Distribution.” Computational Statistics & Data Analysis, 59(1), 41-51. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.csda.2012.10.006")}.
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