lindley.RdEstimates the (1-parameter) Lindley distribution by maximum likelihood estimation.
lindley(link = "loglink", itheta = NULL, zero = NULL)Link function applied to the (positive) parameter.
See Links for more choices.
See CommonVGAMffArguments for information.
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.
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.
This VGAM family function can handle multiple responses (inputted as a matrix). Fisher scoring is implemented.
ldata <- data.frame(y = rlind(n = 1000, theta = exp(3)))
fit <- vglm(y ~ 1, lindley, data = ldata, trace = TRUE, crit = "coef")
#> Iteration 1: coefficients = 0.67029903
#> Iteration 2: coefficients = 1.4587669
#> Iteration 3: coefficients = 2.169915
#> Iteration 4: coefficients = 2.6931435
#> Iteration 5: coefficients = 2.9225853
#> Iteration 6: coefficients = 2.9566605
#> Iteration 7: coefficients = 2.9573048
#> Iteration 8: coefficients = 2.9573051
coef(fit, matrix = TRUE)
#> loglink(theta)
#> (Intercept) 2.957305
Coef(fit)
#> theta
#> 19.24603
summary(fit)
#>
#> Call:
#> vglm(formula = y ~ 1, family = lindley, data = ldata, trace = TRUE,
#> crit = "coef")
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 2.9573 0.0302 97.92 <2e-16 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Name of linear predictor: loglink(theta)
#>
#> Log-likelihood: 1909.152 on 999 degrees of freedom
#>
#> Number of Fisher scoring iterations: 8
#>
#> No Hauck-Donner effect found in any of the estimates
#>