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 |
The Bell distribution has a probability density function that can be written
f(y;s) = s^y * exp(1 - exp(s)) * B_y / y!
for y=0(1)Inf 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.
bdata <- data.frame(y = rbell(1000, shape = loglink(0.5, inverse = TRUE))) bfit <- vglm(y ~ 1, bellff, data = bdata, trace = TRUE, crit = "coef") coef(bfit, matrix = TRUE) Coef(bfit)
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