Description Usage Arguments Details Value Author(s) References Examples
Probability mass, distribution, quantile and function, and random number generator for the Poisson-Binomial distribution with parameter vector pp
(the probability parameter of the component Binomial random variables).
1 2 3 4 | dpoisbinom(x, pp, log_d = FALSE)
ppoisbinom(q, pp, lower_tail = TRUE, log_p = FALSE)
qpoisbinom(p, pp, lower_tail = TRUE, log_p = FALSE)
rpoisbinom(n,pp)
|
x, q |
vector of quantiles. |
p, pp |
vector of probabilities. |
n |
number of random deviates. |
log_d, log_p |
logical; if TRUE, probabilities are given in the log scale. |
lower_tail |
logical; if TRUE (default), probabilities are Pr(X ≤q x), otherwise, Pr(X > x). |
The Poisson-Binomial distribution is the distribution of a sum of n independent and not identically distributed Binomial random variables. It is parameterized by the vector of n possibly distinct probability parameters of these Binomial distributions, and is computed using a discrete Fourier transform. See Hong (2013) for details.
dpoisbinom
gives the mass, ppoisbinom
gives the distribution function, qpoisbinom
gives the quantile function and rpoisbinom
generates random deviates.
If pp
contains values outside of [0,1], an error is returned.
The length of the result is determined by n
in rpoisbinom
, and is the length of the first argument for all other functions.
Shiraito, Y. and Olivella, S. (2017).
Hong, Y. (2013) “On computing the distribution function for the Poisson binomial distribution”. Computational Statistics and Data Analysis, 59, 41–51.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ## Binomial probabilities
pp <- runif(500)
## PMF
dpoisbinom(36, pp)
## CDF
ppoisbinom(36, pp)
## Quantile function
qpoisbinom(0.3, pp)
## Random deviates
rpoisbinom(5, pp)
|
[1] 1.862885e-17
[1] 2.918253e-15
[1] 252
[1] 263 249 263 252 268
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