R: Yule-Simon Family Function

yulesimon {VGAM} | R Documentation

## Yule-Simon Family Function

### Description

Estimating the shape parameter of the Yule-Simon distribution.

### Usage

    yulesimon(lshape = "loglink", ishape = NULL, nsimEIM = 200, zero = NULL)

### Arguments

`lshape` | Link function for the shape parameter, called rho below. See `Links` for more choices and for general information.
`ishape` | Optional initial value for the (positive) parameter. See `CommonVGAMffArguments` for more information. The default is to obtain an initial value internally. Use this argument if the default fails.
`nsimEIM, zero` | See `CommonVGAMffArguments` for more information.

### Details

The probability function is

f(y;rho) = rho*beta(y,rho+1),

where the parameter rho>0, beta is the `beta` function, and y=1,2,.... The function `dyules` computes this probability function. The mean of Y, which is returned as fitted values, is rho/(rho-1) provided rho > 1. The variance of Y is rho^2/((rho-1)^2 (rho-2)) provided rho > 2.

The distribution was named after Udny Yule and Herbert A. Simon. Simon originally called it the Yule distribution. This family function can handle multiple responses.

### Value

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

### Author(s)

T. W. Yee

### References

Simon, H. A. (1955). On a class of skew distribution functions. Biometrika, 42, 425–440.

### See Also

`ryules`, `simulate.vlm`.

### Examples

    ydata <- data.frame(x2 = runif(nn <- 1000))
    ydata <- transform(ydata, y = ryules(nn, shape = exp(1.5 - x2)))
    with(ydata, table(y))
    fit <- vglm(y ~ x2, yulesimon, data = ydata, trace = TRUE)
    coef(fit, matrix = TRUE)
    summary(fit)

[Package VGAM version 1.1-3 Index]