R: Exponential Geometric Distribution Family Function

expgeometric {VGAM} | 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

(1/c) * (1 - s) * e^(-y/c) * (1 - s * e^(-y/c))^(-2)

where y > 0, c > 0 and 0 < s < 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.

### See Also

`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)
    c(with(edata, mean(y)), head(fitted(fit), 1))
    coef(fit, matrix = TRUE)
    Coef(fit)
    summary(fit)

    ## End(Not run)

[Package VGAM version 1.1-3 Index]