VGAM (version 0.8-3)

explogarithmic: Exponential Logarithmic Distribution Family Function

Description

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

Usage

explogarithmic(lscale = "loge", lshape = "logit", escale = list(),
               eshape = list(), iscale = NULL, ishape = NULL,
               tol12 = 1e-05, zero = 1, nsimEIM = 400)

Arguments

lscale, lshape, escale, eshape

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

scale = exp(2); shape = logit(-1, inverse = TRUE);
edata = data.frame(y = rexplog(n = 2000, scale = scale, shape = shape))
fit = vglm(y ~ 1, explogarithmic, edata, trace = TRUE)
c(with(edata, median(y)), head(fitted(fit), 1))
coef(fit, matrix = TRUE)
Coef(fit)
summary(fit)