VGAM (version 1.0-6)

topple: Topp-Leone Distribution Family Function

Description

Estimating the parameter of the Topp-Leone distribution by maximum likelihood estimation.

Usage

topple(lshape = "logit", zero = NULL, gshape = ppoints(8))

Arguments

lshape, zero, gshape

More information is at CommonVGAMffArguments.

Value

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

Details

The Topple distribution has a probability density function that can be written $$f(y;s)=2s(1-y)[y(2-y){]}^{s-1}$$ for $0<y<1$ and shape parameter $0<s<1$. The mean of $Y$ is $1-4^s[\mathrm{\Gamma }(1+s){]}^2/\mathrm{\Gamma }(2+2s)$ (returned as the fitted values).

References

Topp, C. W. and F. C. Leone (1955) A family of J-shaped frequency functions. Journal of the American Statistical Association, 50, 209--219.

See Also

Topple, Triangle.

Examples

# NOT RUN {
tdata <- data.frame(y = rtopple(1000, shape = logit(1, inverse = TRUE)))
tfit <- vglm(y ~ 1, topple, data = tdata, trace = TRUE, crit = "coef")
coef(tfit, matrix = TRUE)
Coef(tfit)
# }