VGAM (version 1.1-1)

explogff: 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.

Value

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

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.

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)
# }