felix.RdEstimates the parameter of a Felix distribution by maximum likelihood estimation.
felix(lrate = "extlogitlink(min = 0, max = 0.5)", imethod = 1)Link function for the parameter,
called \(a\) below;
see Links for more choices and for general information.
See CommonVGAMffArguments.
Valid values are 1, 2, 3 or 4.
The Felix distribution is an important basic Lagrangian distribution. The density function is $$f(y;a) = \frac{ 1 }{((y-1)/2)!} y^{(y-3)/2} a^{(y-1)/2} \exp(-ay) $$ where \(y=1,3,5,\ldots\) and \(0 < a < 0.5\). The mean is \(1/(1-2a)\) (returned as the fitted values). Fisher scoring is implemented.
An object of class "vglmff"
(see vglmff-class).
The object is used by modelling functions
such as vglm
and vgam.
Consul, P. C. and Famoye, F. (2006). Lagrangian Probability Distributions, Boston, USA: Birkhauser.
fdata <- data.frame(y = 2 * rpois(n = 200, 1) + 1) # Not real data!
fit <- vglm(y ~ 1, felix, data = fdata, trace = TRUE, crit = "coef")
#> Iteration 1: coefficients = 0.11480955
#> Iteration 2: coefficients = 0.88005067
#> Iteration 3: coefficients = 0.70127922
#> Iteration 4: coefficients = 0.68326115
#> Iteration 5: coefficients = 0.68309686
#> Iteration 6: coefficients = 0.68309684
coef(fit, matrix = TRUE)
#> extlogitlink(rate, min = 0, max = 0.5)
#> (Intercept) 0.6830968
Coef(fit)
#> rate
#> 0.3322148
summary(fit)
#>
#> Call:
#> vglm(formula = y ~ 1, family = felix, data = fdata, trace = TRUE,
#> crit = "coef")
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 0.6831 0.2118 3.226 0.00126 **
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Name of linear predictor: extlogitlink(rate, min = 0, max = 0.5)
#>
#> Log-likelihood: -350.7791 on 199 degrees of freedom
#>
#> Number of Fisher scoring iterations: 6
#>
#> No Hauck-Donner effect found in any of the estimates
#>