Probability Mass Function of the Zero-Truncated Poisson Distribution

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

Usage

pdf.tp(y, lambda, log.p = FALSE)

Arguments

y

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

lambda

Numeric vector of rate parameters (mean of the Poisson distribution).

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 Poisson 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 Poisson PMF and CDF, respectively. The function uses dpois and ppois internally.

This function automatically vectorizes inputs so that each probability corresponds elementwise to the provided parameter values.

See also

dpois, ppois, and cdf.tp for the corresponding cumulative function.

Examples

# Example: Zero-truncated Poisson probabilities
y <- 1:5
lambda <- 2
pdf.tp(y, lambda)
#> [1] 0.31303529 0.31303529 0.20869019 0.10434510 0.04173804

# Log probabilities
pdf.tp(y, lambda, log.p = TRUE)
#> [1] -1.161439 -1.161439 -1.566904 -2.260052 -3.176342