# posgeomUC: Positive-Geometric Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

Density, distribution function, quantile function and random generation for the positive-geometric distribution.

## Usage

 ```1 2 3 4``` ```dposgeom(x, prob, log = FALSE) pposgeom(q, prob) qposgeom(p, prob) rposgeom(n, prob) ```

## Arguments

 `x, q` vector of quantiles. `p` vector of probabilities. `n` number of observations. Fed into `runif`. `prob` vector of probabilities of success (of an ordinary geometric distribution). Short vectors are recycled. `log` logical.

## Details

The positive-geometric distribution is a geometric distribution but with the probability of a zero being zero. The other probabilities are scaled to add to unity. The mean therefore is 1/prob.

As prob decreases, the positive-geometric and geometric distributions become more similar. Like similar functions for the geometric distribution, a zero value of `prob` is not permitted here.

## Value

`dposgeom` gives the density, `pposgeom` gives the distribution function, `qposgeom` gives the quantile function, and `rposgeom` generates random deviates.

## Author(s)

T. W. Yee

`zageometric`, `zigeometric`, `rgeom`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```prob <- 0.75; y <- rposgeom(n = 1000, prob) table(y) mean(y) # Sample mean 1 / prob # Population mean (ii <- dposgeom(0:7, prob)) cumsum(ii) - pposgeom(0:7, prob) # Should be 0s table(rposgeom(100, prob)) table(qposgeom(runif(1000), prob)) round(dposgeom(1:10, prob) * 1000) # Should be similar ## Not run: x <- 0:5 barplot(rbind(dposgeom(x, prob), dgeom(x, prob)), beside = TRUE, col = c("blue", "orange"), main = paste("Positive geometric(", prob, ") (blue) vs", " geometric(", prob, ") (orange)", sep = ""), names.arg = as.character(x), las = 1, lwd = 2) ## End(Not run) ```