Estimates the two parameters of the generalized Rayleigh distribution by maximum likelihood estimation.
genrayleigh(lscale = "loglink", lshape = "loglink", iscale = NULL, ishape = NULL, tol12 = 1e-05, nsimEIM = 300, zero = 2)
Link function for the two positive parameters, scale and shape.
Numeric. Optional initial values for the scale and shape parameters.
Numeric and positive. Tolerance for testing whether the second shape parameter is either 1 or 2. If so then the working weights need to handle these singularities.
The generalized Rayleigh distribution has density function
(2*s*y/b^2) * e^(-(y/b)^2) * (1 - e^(-(y/b)^2))^(s-1)
where y > 0 and the two parameters, b and s, are positive. The mean cannot be expressed nicely so the median is returned as the fitted values. Applications of the generalized Rayleigh distribution include modeling strength data and general lifetime data. Simulated Fisher scoring is implemented.
An object of class
The object is used by modelling functions such as
scale as the reciprocal of the scale parameter
used by Kundu and Raqab (2005).
J. G. Lauder and T. W. Yee
Kundu, D., Raqab, M. C. (2005). Generalized Rayleigh distribution: different methods of estimations. Computational Statistics and Data Analysis, 49, 187–200.
Scale <- exp(1); shape <- exp(1) rdata <- data.frame(y = rgenray(n = 1000, scale = Scale, shape = shape)) fit <- vglm(y ~ 1, genrayleigh, data = rdata, trace = TRUE) c(with(rdata, mean(y)), head(fitted(fit), 1)) coef(fit, matrix = TRUE) Coef(fit) summary(fit)
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