Continuous parameter binomial distribution functions

Density, distribution function, and quantile function for the continuous parameter binomial (CPB), and its zero-truncated form. The CPB has a hard ceiling at \(\lfloor \lambda/(1-\alpha) \rfloor\); probability above it is zero. Complements the simulator rcpb().

Usage

dcpb(x, lambda, alpha, truncated = FALSE, log = FALSE)

pcpb(q, lambda, alpha, truncated = FALSE, lower.tail = TRUE, log.p = FALSE)

qcpb(p, lambda, alpha, truncated = FALSE, lower.tail = TRUE, log.p = FALSE)

Arguments

x, q

Vector of quantiles (non-negative integers).

lambda

Mean parameter (scalar or vector, recycled).

alpha

Shape parameter in (0, 1).

truncated

If TRUE, use the zero-truncated CPB. Where the implied ceiling lambda / (1 - alpha) is below 1 the CPB puts all its mass on 0, and its zero-truncated form is the point mass at 1, the zero-truncated distribution for every ceiling in [1, 2).

log, log.p

If TRUE, probabilities are given as log.

lower.tail

If TRUE (default), probabilities are \(P(X \le x)\).

p

Vector of probabilities.

Value

dcpb a density, pcpb a distribution function, qcpb a quantile.

See also

rcpb()

Examples

dcpb(0:5, lambda = 3, alpha = 0.5)
#> [1] 0.015625 0.093750 0.234375 0.312500 0.234375 0.093750
pcpb(3, lambda = 3, alpha = 0.5)
#> [1] 0.65625
qcpb(0.9, lambda = 3, alpha = 0.5)
#> [1] 5