R: Exponential Poisson Distribution Family Function

exppoisson {VGAM} | R Documentation

## Exponential Poisson Distribution Family Function

### Description

Estimates the two parameters of the exponential Poisson distribution by maximum likelihood estimation.

### Usage

    exppoisson(lrate = "loge", lshape = "loge",
               irate = 2, ishape = 1.1,  zero = NULL)

### Arguments

`lshape, lrate` | Link function for the two positive parameters. See `Links` for more choices.
`ishape, irate` | Numeric. Initial values for the `shape` and `rate` parameters. Currently this function is not intelligent enough to obtain better initial values.
`zero` | See `CommonVGAMffArguments`.

### Details

The exponential Poisson distribution has density function

f(y; a = shape, b = rate) = (a*b/(1 - e^(-a))) * e^{-a - b*y + a * e^(-b*y)}

where y > 0, and the parameters shape, a, and rate, b, are positive. The distribution implies a population facing discrete hazard rates which are multiples of a base hazard. This VGAM family function requires the `hypergeo` package (to use their `genhypergeo` function). The median is returned as the fitted value.

### Value

An object of class `"vglmff"` (see `vglmff-class`). The object is used by modelling functions such as `vglm` and `vgam`.

### Warning

This VGAM family function does not work properly!

### Author(s)

J. G. Lauder, jamesglauder@gmail.com

### References

Kus, C., (2007). A new lifetime distribution. Computational Statistics and Data Analysis, 51, 4497–4509.

### See Also

`dexppois`, `exponential`, `poisson`.

### Examples

    ## Not run:
    shape <- exp(1); rate <- exp(2)
    rdata <- data.frame(y = rexppois(n = 1000, rate = rate, shape = shape))
    library("hypergeo")  # Required!
    fit <- vglm(y ~ 1, exppoisson, data = rdata, trace = FALSE, maxit = 1200)
    c(with(rdata, median(y)), head(fitted(fit), 1))
    coef(fit, matrix = TRUE)
    Coef(fit)
    summary(fit)

    ## End(Not run)

[Package VGAM version 1.0-3 Index]