R: Exponential Logarithmic Distribution Family Function

explogff {VGAM} | R Documentation

## Exponential Logarithmic Distribution Family Function

### Description

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

### Usage

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

### Arguments

`lscale, lshape` | See `CommonVGAMffArguments` for information.
`tol12` | Numeric. Tolerance for testing whether a parameter has value 1 or 2.
`iscale, ishape, zero, nsimEIM` | See `CommonVGAMffArguments`.

### Details

The exponential logarithmic distribution has density function

(1/(-log(p))) * (((1/c) * (1 - s) * e^(-y/c)) / (1 - (1 - s) * e^(-y/c)))

where y > 0, scale parameter c > 0, and shape parameter 0 < s < 1. The mean, ((-polylog(2, 1 - p) * c) / log(s) is not returned as the fitted values. Note the median is c * log(1 + sqrt(s)) and it is currently returned as the fitted values. 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 rate parameter used by Tahmasabi and Sadegh (2008).

Yet to do: find a `polylog()` function.

### Author(s)

J. G. Lauder and T. W .Yee

### References

Tahmasabi, R., Sadegh, R. (2008). A two-parameter lifetime distribution with decreasing failure rate. Computational Statistics and Data Analysis, 52, 3889–3901.

### See Also

`dexplog`, `exponential`,

### Examples

    ## Not run:  Scale <- exp(2); shape <- logitlink(-1, inverse = TRUE)
    edata <- data.frame(y = rexplog(n = 2000, scale = Scale, shape = shape))
    fit <- vglm(y ~ 1, explogff, data = edata, trace = TRUE)
    c(with(edata, median(y)), head(fitted(fit), 1))
    coef(fit, matrix = TRUE)
    Coef(fit)
    summary(fit)

    ## End(Not run)

[Package VGAM version 1.1-3 Index]