R: The Exponential Poisson Distribution

exppois {VGAM} | R Documentation

## The Exponential Poisson Distribution

### Description

Density, distribution function, quantile function and random generation for the exponential poisson distribution.

### Usage

    dexppois(x, rate = 1, shape, log = FALSE)
    pexppois(q, rate = 1, shape, lower.tail = TRUE, log.p = FALSE)
    qexppois(p, rate = 1, shape, lower.tail = TRUE, log.p = FALSE)
    rexppois(n, rate = 1, shape)

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations. If `length(n) > 1` then the length is taken to be the number required.
`shape, rate` | positive parameters.
`log` | Logical. If `log = TRUE` then the logarithm of the density is returned.
`lower.tail, log.p` | Same meaning as in `pnorm` or `qnorm`.

### Details

See `exppoisson`, the VGAM family function for estimating the parameters, for the formula of the probability density function and other details.

### Value

`dexppois` gives the density, `pexppois` gives the distribution function, `qexppois` gives the quantile function, and `rexppois` generates random deviates.

### Author(s)

Kai Huang and J. G. Lauder

### See Also

`exppoisson`.

### Examples

    ## Not run:  rate <- 2; shape <- 0.5; nn <- 201
    x <- seq(-0.05, 1.05, len = nn)
    plot(x, dexppois(x, rate = rate, shape), type = "l", las = 1, ylim = c(0, 3),
         ylab = paste("fexppoisson(rate = ", rate, ", shape = ", shape, ")"),
         col = "blue", cex.main = 0.8,
         main = "Blue is the density, orange the cumulative distribution function",
         sub = "Purple lines are the 10,20,...,90 percentiles")
    lines(x, pexppois(x, rate = rate, shape), col = "orange")
    probs <- seq(0.1, 0.9, by = 0.1)
    Q <- qexppois(probs, rate = rate, shape)
    lines(Q, dexppois(Q, rate = rate, shape), col = "purple", lty = 3, type = "h")
    lines(Q, pexppois(Q, rate = rate, shape), col = "purple", lty = 3, type = "h")
    abline(h = probs, col = "purple", lty = 3); abline(h = 0, col = "gray50")
    max(abs(pexppois(Q, rate = rate, shape) - probs))  # Should be 0

    ## End(Not run)

[Package VGAM version 1.1-3 Index]