# bellff: Bell Distribution Family Function In VGAMdata: Data Supporting the 'VGAM' Package

 bellff R Documentation

## Bell Distribution Family Function

### Description

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

### Usage

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

### Arguments

 `lshape, zero, gshape` More information is at `CommonVGAMffArguments`.

### Details

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.

### Value

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

T. W. Yee

### References

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.

`bell`, `dbell`, `poissonff`.

### Examples

```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)
```

VGAMdata documentation built on March 18, 2022, 8:03 p.m.