Topp-Leone Distribution Family Function
Estimating the parameter of the Topp-Leone distribution by maximum likelihood estimation.
topple(lshape = "logitlink", zero = NULL, gshape = ppoints(8),
parallel = FALSE, type.fitted = c("mean", "percentiles", "Qlink"),
percentiles = 50)lshape, gshape |
Details at |
zero, parallel |
Details at |
type.fitted, percentiles |
See |
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).
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
Fisher-scoring and Newton-Raphson are the same here. A related distribution is the triangle distribution. This VGAM family function handles multiple responses.
T. W. Yee
Topp, C. W. and F. C. Leone (1955). A family of J-shaped frequency functions. Journal of the American Statistical Association, 50, 209–219.
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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