Cumulative distribution function of the Beta-Binomial distribution

Computes the CDF \(P(Y \le q)\) by summing the PMF from 0 to floor(q), element-wise.

Usage

pbetabinom(q, n, mu, kappa, lower.tail = TRUE)

Arguments

q

Numeric vector of quantiles.

n

Integer vector of trial sizes (\(n \ge 0\)).

mu

Numeric vector of means, each in \([0, 1]\).

kappa

Numeric vector of concentrations, each \(> 0\).

lower.tail

Logical; if TRUE (default), returns \(P(Y \le q)\); otherwise \(P(Y > q)\).

Value

A numeric vector of probabilities.

Details

Numerical stability is maintained by performing the summation in the log domain using the log-sum-exp trick.

References

Ghosal, S., Ghosh, S., and Moores, M. (2020). “Hierarchical beta-binomial models for batch effects in cytometry data.” Journal of the Royal Statistical Society: Series A, 183(4), 1579–1601.

See also

Other distributions: compute_p0(), compute_ztbb_mean(), dbetabinom(), dhurdle_betabinom(), dztbetabinom(), hurdle_mean(), hurdle_variance(), rbetabinom(), rhurdle_betabinom(), rztbetabinom()

Examples

# CDF at each value
pbetabinom(0:5, n = 5, mu = 0.3, kappa = 10)
#> [1] 0.2307692 0.5454545 0.7972028 0.9370629 0.9895105 1.0000000

# Upper tail
pbetabinom(2, n = 5, mu = 0.3, kappa = 10, lower.tail = FALSE)
#> [1] 0.2027972