topple {VGAM} | R Documentation |
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 |
zero , parallel |
Details at |
type.fitted , percentiles |
See |
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
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)