R: Topp-Leone Distribution Family Function

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

### Arguments

`lshape, gshape` | Details at `CommonVGAMffArguments`.
`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, shape = logitlink(1, inverse = TRUE)))
    tfit <- vglm(y ~ 1, topple, data = tdata, trace = TRUE, crit = "coef")
    coef(tfit, matrix = TRUE)
    Coef(tfit)

[Package VGAM version 1.1-3 Index]