Conditional mean of the zero-truncated Beta-Binomial

Returns the conditional mean of the zero-truncated Beta-Binomial, \(E[Y \mid Y > 0] = n \mu / (1 - p_0)\).

Usage

compute_ztbb_mean(n, mu, kappa)

Arguments

n

Integer vector of trial sizes (\(n \ge 1\)).

mu

Numeric vector of means in \((\varepsilon, 1 - \varepsilon)\).

kappa

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

Value

A numeric vector of conditional means.

Details

Requires \(n \ge 1\) and \(\mu \in (\varepsilon, 1 - \varepsilon)\) so that the zero-truncated distribution is well-defined (i.e., \(p_0 < 1\)).

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(), dbetabinom(), dhurdle_betabinom(), dztbetabinom(), hurdle_mean(), hurdle_variance(), pbetabinom(), rbetabinom(), rhurdle_betabinom(), rztbetabinom()

Examples

# Compare analytical mean with empirical mean
compute_ztbb_mean(10, mu = 0.3, kappa = 5)
#> [1] 3.495269

set.seed(1)
mean(rztbetabinom(10000, n = 10, mu = 0.3, kappa = 5))
#> [1] 3.4795