# pospoisUC: Positive-Poisson Distribution In VGAMdata: Data Supporting the 'VGAM' Package

 Pospois R Documentation

## Positive-Poisson Distribution

### Description

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

### Usage

```dpospois(x, lambda, log = FALSE)
ppospois(q, lambda)
qpospois(p, lambda)
rpospois(n, lambda)
```

### Arguments

 `x, q` vector of quantiles. `p` vector of probabilities. `n` number of observations. Fed into `runif`. `lambda` vector of positive means (of an ordinary Poisson distribution). Short vectors are recycled. `log` logical.

### Details

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

lambda / (1-exp(-lambda)).

As lambda increases, the positive-Poisson and Poisson distributions become more similar. Unlike similar functions for the Poisson distribution, a zero value of `lambda` returns a `NaN`.

### Value

`dpospois` gives the density, `ppospois` gives the distribution function, `qpospois` gives the quantile function, and `rpospois` generates random deviates.

### Note

These functions are or are likely to be deprecated. Use `Gaitdpois` instead.

The family function `pospoisson` estimates lambda by maximum likelihood estimation.

### Author(s)

T. W. Yee

`Gaitdpois`, `pospoisson`, `zapoisson`, `zipoisson`, `rpois`.

### Examples

```lambda <- 2; y = rpospois(n = 1000, lambda)
table(y)
mean(y)  # Sample mean
lambda / (1 - exp(-lambda))  # Population mean

(ii <- dpospois(0:7, lambda))
cumsum(ii) - ppospois(0:7, lambda)  # Should be 0s
table(rpospois(100, lambda))

table(qpospois(runif(1000), lambda))
round(dpospois(1:10, lambda) * 1000)  # Should be similar

## Not run:  x <- 0:7
barplot(rbind(dpospois(x, lambda), dpois(x, lambda)),
beside = TRUE, col = c("blue", "orange"),
main = paste("Positive Poisson(", lambda, ") (blue) vs",
" Poisson(", lambda, ") (orange)", sep = ""),
names.arg = as.character(x), las = 1, lwd = 2)
## End(Not run)
```

VGAMdata documentation built on March 18, 2022, 8:03 p.m.