topple: Topp-Leone Distribution Family Function

In VGAM: Vector Generalized Linear and Additive Models

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"))

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.

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).

Value

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

Note

Fisher-scoring and Newton-Raphson are the same here. A related distribution is the triangle distribution. This VGAM family function handles multiple responses.

Author(s)

T. W. Yee

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

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)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.