yulesimon {VGAM} | R Documentation

## Yule-Simon Family Function

### Description

Estimating the parameter of the Yule-Simon distribution.

### Usage

    yulesimon(link="loge", earg=list(), irho=NULL, nsimEIM=200)

### Arguments

`link, earg` | Link function and extra argument for the rho parameter. See `Links` for more choices and for general information.
`irho` | 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` | See `CommonVGAMffArguments` for more information.

### Details

The probability function is

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

where the parameter rho>0 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.

### 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`.

### Examples

    x = runif(n <- 1000)
    y = ryules(n, rho=exp(1.5-x))
    table(y)
    fit = vglm(y ~ x, yulesimon, trace=TRUE)
    coef(fit, matrix=TRUE)
    summary(fit)

[Package VGAM version 0.7-9 Index]