# exppoisson: Exponential Poisson Distribution Family Function In VGAM: Vector Generalized Linear and Additive Models

## Description

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

## Usage

 ```1 2``` ```exppoisson(lrate = "loglink", lshape = "loglink", 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.

`dexppois`, `exponential`, `poisson`.
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```## 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) ```