psinib: Distribution of Sum of Independent Non-Identical Binomial...

In sinib: Sum of Independent Non-Identical Binomial Random Variables

Description

Density, 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 Xr, r = 1,...,R.

S = X1+X2+...XR

size and prob should both be vectors of length R. The first elements of size and prob specifies X1, the second elements specifies X2, 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 <- as.integer(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 <- as.integer(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)

sinib documentation built on May 2, 2019, 6:04 a.m.