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 0.7-7 Index]