Exponential Geometric Distribution Family Function

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

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

Arguments

lscale, lshape

Link function for the two parameters. See Links for more choices.

iscale, ishape

Numeric. Optional initial values for the scale and shape parameters.

tol12

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

zero, nsimEIM

See CommonVGAMffArguments.

Details

The exponential geometric distribution has density function $$f(y; c = scale, s = shape) = (1/c) (1 - s) e^{-y/c} (1 - s e^{-y/c})^{-2}$$ where \(y > 0\), \(c > 0\) and \(s \in (0, 1)\). The mean, \((c (s - 1)/ s) \log(1 - s)\) is returned as the fitted values. Note the median is \(c \log(2 - s)\). 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.

References

Adamidis, K., Loukas, S. (1998). A lifetime distribution with decreasing failure rate. Statistics and Probability Letters, 39, 35–42.

Author

J. G. Lauder and T. W. Yee

Note

We define scale as the reciprocal of the scale parameter used by Adamidis and Loukas (1998).

See also

dexpgeom, exponential, geometric.

Examples

if (FALSE) { # \dontrun{
Scale <- exp(2); shape = logitlink(-1, inverse = TRUE);
edata <- data.frame(y = rexpgeom(n = 2000, scale = Scale, shape = shape))
fit <- vglm(y ~ 1, expgeometric, edata, trace = TRUE)
c(with(edata, mean(y)), head(fitted(fit), 1))
coef(fit, matrix = TRUE)
Coef(fit)
summary(fit)
} # }