bellff: Bell Distribution Family Function

View source: R/family.vd1.R

bellffR Documentation

Bell Distribution Family Function


Estimating the shape parameter of the Bell distribution by maximum likelihood estimation.


bellff(lshape = "loglink", zero = NULL, gshape = expm1(1.6 * ppoints(7)))


lshape, zero, gshape

More information is at CommonVGAMffArguments.


The Bell distribution has a probability density function that can be written

f(y;s) = \frac{s^y \exp(1 - e^s) B_y}{y!}

for y=0(1)\infty and shape parameter 0<s. The mean of Y is \exp(s) s (returned as the fitted values). Fisher-scoring is used. This VGAM family function handles multiple responses.

The function bell returns the first 218 Bell numbers as finite numbers, and returns Inf when its argument has a higher value. Hence this VGAM family function can only handle low-value counts of less than 219.


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


T. W. Yee


Castellares, F. and Ferrari, S. L. P. and Lemonte, A. J. (2018). On the Bell distribution and its associated regression model for count data. Applied Mathematical Modelling, 56, 172–185.

See Also

bell, dbell, poissonff.


bdata <- data.frame(y = rbell(1000, loglink(0.5, inverse = TRUE)))
bfit <- vglm(y ~ 1, bellff, bdata, trace = TRUE, crit = "coef")
coef(bfit, matrix = TRUE)

VGAMdata documentation built on Sept. 18, 2023, 9:08 a.m.