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VGAM (version 1.1-1)

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
zero, parallel
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)=2s(1y)[y(2y)]s1 for 0<y<1 and shape parameter 0<s<1. The mean of Y is 14s[Γ(1+s)]2/Γ(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

Run this code
# 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)
# }

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