VGAM (version 1.1-4)

topple: Topp-Leone Distribution Family Function

Description

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

Usage

topple(lshape = "logitlink", zero = NULL, gshape = ppoints(8),
       parallel = FALSE, type.fitted = c("mean", "percentiles", "Qlink"),
       percentiles = 50)

Arguments

lshape, gshape

Details at CommonVGAMffArguments.

zero, parallel

Details at CommonVGAMffArguments.

type.fitted, percentiles

See CommonVGAMffArguments for information. Using "Qlink" is for quantile-links in VGAMextra.

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 $$f(y;s) = 2 s (1 - y) [y (2-y)]^{s-1}$$ for \(0<y<1\) and shape parameter \(0<s<1\). The mean of \(Y\) is \(1 - 4^s [\Gamma(1+s)]^2 / \Gamma(2 + 2s)\) (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 = logitlink(1, inverse = TRUE)))
tfit <- vglm(y ~ 1, topple, data = tdata, trace = TRUE, crit = "coef")
coef(tfit, matrix = TRUE)
Coef(tfit)
# }