R: Positive-Geometric Distribution

Posgeom {VGAM} | R Documentation

## Positive-Geometric Distribution

### Description

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

### Usage

    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

### See Also

`zageometric`, `zigeometric`, `rgeom`.

### Examples

    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)

[Package VGAM version 1.0-3 Index]