1-parameter Gamma Distribution
Estimates the (1-parameter) Lindley distribution by maximum likelihood estimation.
lindley(link = "loglink", itheta = NULL, zero = NULL)
link |
Link function applied to the (positive) parameter.
See |
itheta, zero |
See |
The density function is given by
f(y; theta) = theta^2 * (1 + y) * exp(-theta * y) / (1 + theta)
for theta > 0 and y > 0. The mean of Y (returned as the fitted values) is mu = (theta + 2) / (theta * (theta + 1)). The variance is (theta^2 + 4 * theta + 2) / (theta * (theta + 1))^2.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm
and vgam.
This VGAM family function can handle multiple responses (inputted as a matrix). Fisher scoring is implemented.
T. W. Yee
Lindley, D. V. (1958). Fiducial distributions and Bayes' theorem. Journal of the Royal Statistical Society, Series B, Methodological, 20, 102–107.
Ghitany, M. E. and Atieh, B. and Nadarajah, S. (2008). Lindley distribution and its application. Math. Comput. Simul., 78, 493–506.
ldata <- data.frame(y = rlind(n = 1000, theta = exp(3))) fit <- vglm(y ~ 1, lindley, data = ldata, trace = TRUE, crit = "coef") coef(fit, matrix = TRUE) Coef(fit) summary(fit)
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