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VGAM (version 1.1-12)

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, percentiles = 50,
       type.fitted = c("mean", "percentiles", "Qlink"))

Value

An object of class "vglmff"

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

Arguments

lshape, gshape

Details at CommonVGAMffArguments. The CIA link is loglink, for shape approaching unity.

zero, parallel

Details at CommonVGAMffArguments.

type.fitted, percentiles

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

Author

T. W. Yee

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

Run this code
tdata <- data.frame(y = rtopple(1000, logitlink(1, inverse = TRUE)))
tfit <- vglm(y ~ 1, topple, tdata, trace = TRUE, crit = "coef")
coef(tfit, matrix = TRUE)
Coef(tfit)

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