Expected value under the Hurdle Beta-Binomial

Computes the unconditional mean $$ E[Y] = q \cdot \frac{n \mu}{1 - p_0}, $$ where \(p_0 = P(Y = 0)\) under the (untruncated) Beta-Binomial.

Usage

hurdle_mean(n, q, mu, kappa)

Arguments

n

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

q

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

mu

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

kappa

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

Value

A numeric vector of expected values.

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_variance(), pbetabinom(), rbetabinom(), rhurdle_betabinom(), rztbetabinom()

Examples

hurdle_mean(n = 10, q = 0.7, mu = 0.3, kappa = 5)
#> [1] 2.446688

# q = 0 always gives 0
hurdle_mean(n = 10, q = 0, mu = 0.3, kappa = 5)
#> [1] 0