Estimates the two parameters of the exponential logarithmic distribution by maximum likelihood estimation.
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Numeric. Tolerance for testing whether a parameter has value 1 or 2.
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
The object is used by modelling functions such as
scale as the reciprocal of the rate parameter
used by Tahmasabi and Sadegh (2008).
Yet to do: find a
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.
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## 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) Coef(fit) summary(fit) ## End(Not run)
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