explogarithmic {VGAM} | R Documentation |
Estimates the two parameters of the exponential logarithmic distribution by maximum likelihood estimation.
explogarithmic(lscale = "loge", lshape = "logit", escale = list(), eshape = list(), iscale = NULL, ishape = NULL, tol12 = 1e-05, zero = 1, nsimEIM = 400)
lscale, lshape, escale, eshape |
See |
tol12 |
Numeric. Tolerance for testing whether a parameter has value 1 or 2. |
iscale, ishape, zero, nsimEIM |
The exponential logarithmic distribution has density function
(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 0 < s < 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.
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)