# explogff: Exponential Logarithmic Distribution Family Function In VGAM: Vector Generalized Linear and Additive Models

 explogff 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

f(y; c, s) = (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 s \in (0, 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.

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)