explogff: Exponential Logarithmic Distribution Family Function

View source: R/family.others.R

explogffR Documentation

Exponential Logarithmic Distribution Family Function


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


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


lscale, lshape

See CommonVGAMffArguments for information.


Numeric. Tolerance for testing whether a parameter has value 1 or 2.

iscale, ishape, zero, nsimEIM

See CommonVGAMffArguments.


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.


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


We define scale as the reciprocal of the rate parameter used by Tahmasabi and Sadegh (2008).

Yet to do: find a polylog() function.


J. G. Lauder and T. W .Yee


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,


## 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)

## End(Not run)

VGAM documentation built on Sept. 19, 2023, 9:06 a.m.