Package 'sinib'

Sum of Independent Non-Identical Binomial Random Variables

Description

Density function, distribution function, quantile function and random number generation for the sum of independent non-identical binomial distribution with parameters size and prob. For more see: Boxiang Liu and Thomas Quertermous (2018) The R Journal <https://journal.r-project.org/archive/2018/RJ-2018-011/index.html>.

Author(s)

Boxiang Liu

Maintainer: Boxiang Liu <[email protected]>

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Distribution of Sum of Independent Non-Identical Binomial Random Variables

Description

Density function, distribution function, quantile function, and random number generation for the sum of independent non-identical binomial random variables

Usage

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

dsinib(x, size, prob, log = FALSE)

rsinib(n, size, prob)

qsinib(p, size, prob)

Arguments

size	integer vector of number of trials (see detail).
prob	numeric vector of success probabilities (see detail).
lower.tail	logical; if TRUE, probabilities are $P[S<=s]$, otherwise, $P[S>s]$.
x, q	integer vector of quantiles.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
n	numeric scalar to indicate number of observations.
p	numeric vector of probabilities.

Details

Suppose S is a random variable formed by summing R independent non-identical random variables $X_r$, $r = 1,...,R$.

$S = \sum_{r=1}^R X_r$

size and prob should both be vectors of length R. The first elements of size and prob specifies $X_1$, the second elements specifies $X_2$, so on and so forth. The probability $F(S)$ is calculated using Daniels' second-order continuity-corrected saddlepoint approximation. The density $p(S)$ is calculated using second-order saddlepoint mass approximation with Butler's normalization.

Value

qsinib gives the cumulative distribution of sum of independent non-identical random variables.

Source

See Eisinga et al (2012) Saddlepoint approximations for the sum of independent non-identically distributed binomial random variables. Available from http://onlinelibrary.wiley.com/doi/10.1111/stan.12002/full

Examples

# Calculating the density and probability:
size <- c(12, 14, 4, 2, 20, 17, 11, 1, 8, 11)
prob <- c(0.074, 0.039, 0.095, 0.039, 0.053, 0.043, 0.067, 0.018, 0.099, 0.045)
q <- x <- seq(1, 19, 2)
dsinib(x, size, prob)
psinib(q, size, prob)

# Generating random samples:
rsinib(100, size, prob)

# Calculating quantiles:
p <- psinib(q, size, prob) 
qsinib(p, size, prob)

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