Felix Distribution Family Function

Estimates the parameter of a Felix distribution by maximum likelihood estimation.

Usage

felix(lrate = "extlogitlink(min = 0, max = 0.5)", imethod = 1)

Arguments

lrate

Link function for the parameter, called $a$ below; see Links for more choices and for general information.

imethod

See CommonVGAMffArguments. Valid values are 1, 2, 3 or 4.

Details

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.

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm and vgam.

References

Consul, P. C. and Famoye, F. (2006). Lagrangian Probability Distributions, Boston, USA: Birkhauser.

Author

T. W. Yee

Examples

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 = 0.085201744
#> Iteration 2: coefficients = 0.87593939
#> Iteration 3: coefficients = 0.68805708
#> Iteration 4: coefficients = 0.66803258
#> Iteration 5: coefficients = 0.66782939
#> Iteration 6: coefficients = 0.66782937
coef(fit, matrix = TRUE)
#>             extlogitlink(rate, min = 0, max = 0.5)
#> (Intercept)                              0.6678294
Coef(fit)
#>      rate 
#> 0.3305085 
summary(fit)
#> 
#> Call:
#> vglm(formula = y ~ 1, family = felix, data = fdata, trace = TRUE, 
#>     crit = "coef")
#> 
#> Coefficients: 
#>             Estimate Std. Error z value Pr(>|z|)   
#> (Intercept)   0.6678     0.2113   3.161  0.00157 **
#> ---
#> 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: -346.3936 on 199 degrees of freedom
#> 
#> Number of Fisher scoring iterations: 6 
#>