TruncPoisson function

Truncated Poisson distribution

Density, distribution function, quantile function and random generation for the truncated Poisson distribution.

dtpois(x, lambda, a = -Inf, b = Inf, log = FALSE)

ptpois(q, lambda, a = -Inf, b = Inf, lower.tail = TRUE, log.p = FALSE)

qtpois(p, lambda, a = -Inf, b = Inf, lower.tail = TRUE, log.p = FALSE)

rtpois(n, lambda, a = -Inf, b = Inf)

Arguments

• x, q: vector of quantiles.

• lambda: vector of (non-negative) means.

• a, b: lower and upper truncation points (a < x <= b).

• log, log.p: logical; if TRUE, probabilities p are given as log(p).

• lower.tail: logical; if TRUE (default), probabilities are $P[X \le x]$

  otherwise, $P[X > x]$.

• p: vector of probabilities.

• n: number of observations. If length(n) > 1, the length is taken to be the number required.

Examples

x <- rtpois(1e5, 14, 16)
xx <- seq(-1, 50)
plot(prop.table(table(x)))
lines(xx, dtpois(xx, 14, 16), col = "red")
hist(ptpois(x, 14, 16))

xx <- seq(0, 50, by = 0.01)
plot(ecdf(x))
lines(xx, ptpois(xx, 14, 16), col = "red", lwd = 2)

uu <- seq(0, 1, by = 0.001)
lines(qtpois(uu, 14, 16), uu, col = "blue", lty = 2)

# Zero-truncated Poisson

x <- rtpois(1e5, 5, 0)
xx <- seq(-1, 50)
plot(prop.table(table(x)))
lines(xx, dtpois(xx, 5, 0), col = "red")
hist(ptpois(x, 5, 0))

xx <- seq(0, 50, by = 0.01)
plot(ecdf(x))
lines(xx, ptpois(xx, 5, 0), col = "red", lwd = 2)
lines(qtpois(uu, 5, 0), uu, col = "blue", lty = 2)

References

Plackett, R.L. (1953). The truncated Poisson distribution. Biometrics, 9(4), 485-488.

Singh, J. (1978). A characterization of positive Poisson distribution and its statistical application. SIAM Journal on Applied Mathematics, 34(3), 545-548.

Dalgaard, P. (May 1, 2005). [R] simulate zero-truncated Poisson distribution. R-help mailing list. https://stat.ethz.ch/pipermail/r-help/2005-May/070680.html