Computes the PMF of the two-part hurdle model: $$ P(Y = 0) = 1 - q, \quad P(Y = y) = q \cdot f_{\text{ZT}}(y \mid n, \mu, \kappa), \quad y \in \{1, \ldots, n\}, $$ where \(f_{\text{ZT}}\) is the zero-truncated Beta-Binomial PMF.
Arguments
- y
Integer vector of observed counts.
- 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, each in \((\varepsilon, 1 - \varepsilon)\).
- kappa
Numeric vector of concentrations (\(> 0\)).
- log
Logical; if
TRUE, return log-probabilities.
Details
The structural zero probability \(1 - q\) is computed as
log1p(-q) in the log domain for numerical stability when
\(q\) is near 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(),
compute_ztbb_mean(),
dbetabinom(),
dztbetabinom(),
hurdle_mean(),
hurdle_variance(),
pbetabinom(),
rbetabinom(),
rhurdle_betabinom(),
rztbetabinom()
Examples
# PMF over full support
dhurdle_betabinom(0:5, n = 5, q = 0.7, mu = 0.4, kappa = 8)
#> [1] 0.30000000 0.20157439 0.21708011 0.16600244 0.08872544 0.02661763
# Should sum to 1
sum(dhurdle_betabinom(0:5, n = 5, q = 0.7, mu = 0.4, kappa = 8))
#> [1] 1
# Log scale
dhurdle_betabinom(0:5, n = 5, q = 0.7, mu = 0.4, kappa = 8, log = TRUE)
#> [1] -1.203973 -1.601597 -1.527489 -1.795753 -2.422209 -3.626181