VGAM (version 1.1-9)

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)

Value

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

and vgam.

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.

Author

J. G. Lauder and T. W .Yee

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

if (FALSE)  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)