Probability Mass Function of the Zero-Truncated Negative Binomial Distribution

Computes the probability mass function (PMF) or log-PMF for the zero-truncated negative binomial (TNB) distribution. This version excludes zeros and rescales the probabilities accordingly so that they sum to one over positive counts only.

Usage

pdf.tnb(y, mu, size, log.p = FALSE)

Arguments

y

Numeric vector of observed count values (y > 0).

mu

Numeric vector of mean parameters for the negative binomial distribution.

size

Numeric vector of shape (dispersion) parameters.

log.p

Logical; if TRUE, returns log probabilities instead of probabilities.

Value

A numeric vector of probabilities (or log-probabilities if log.p = TRUE).

Details

The zero-truncated negative binomial probability for an observation \(y > 0\) is: $$ P(Y = y \mid Y > 0) = \frac{P(Y = y)}{1 - P(Y = 0)} $$ where \(P(Y = y)\) and \(P(Y = 0)\) are evaluated using the standard negative binomial PMF and CDF, respectively. The implementation uses dnbinom and pnbinom for computation.

The function automatically vectorizes inputs, ensuring that the output corresponds elementwise to each set of parameters.

See also

dnbinom, pnbinom, and cdf.tnb for the corresponding cumulative function.

Examples

# Example: Zero-truncated negative binomial probabilities
y <- 1:5
mu <- 2
size <- 1.5
pdf.tnb(y, mu, size)
#> [1] 0.33426968 0.23876406 0.15917604 0.10232745 0.06432011

# Log probabilities
pdf.tnb(y, mu, size, log.p = TRUE)
#> [1] -1.095807 -1.432279 -1.837745 -2.279577 -2.743883