# expgeometric: Exponential Geometric Distribution Family Function In VGAM: Vector Generalized Linear and Additive Models

 expgeometric R Documentation

## Exponential Geometric Distribution Family Function

### Description

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

### Usage

expgeometric(lscale = "loglink", lshape = "logitlink",
iscale = NULL,   ishape = NULL,
tol12 = 1e-05, zero = 1, nsimEIM = 400)


### Arguments

 lscale, lshape Link function for the two parameters. See Links for more choices. iscale, ishape Numeric. Optional initial values for the scale and shape parameters. tol12 Numeric. Tolerance for testing whether a parameter has value 1 or 2. zero, nsimEIM See CommonVGAMffArguments.

### Details

The exponential geometric distribution has density function

f(y; c = scale, s = shape) = (1/c) (1 - s) e^{-y/c} (1 - s e^{-y/c})^{-2}

where y > 0, c > 0 and s \in (0, 1). The mean, (c (s - 1)/ s) \log(1 - s) is returned as the fitted values. Note the median is c \log(2 - s). Simulated Fisher scoring is implemented.

### Value

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

### Note

We define scale as the reciprocal of the scale parameter used by Adamidis and Loukas (1998).

### Author(s)

J. G. Lauder and T. W. Yee

### References

Adamidis, K., Loukas, S. (1998). A lifetime distribution with decreasing failure rate. Statistics and Probability Letters, 39, 35–42.

dexpgeom, exponential, geometric.

### Examples

## Not run:
Scale <- exp(2); shape = logitlink(-1, inverse = TRUE);
edata <- data.frame(y = rexpgeom(n = 2000, scale = Scale, shape = shape))
fit <- vglm(y ~ 1, expgeometric, edata, trace = TRUE)