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 = "logit", zero = NULL, gshape = ppoints(8))

### Arguments

`lshape, zero, gshape` | More information is at `CommonVGAMffArguments`.

### 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 = logit(1, inverse = TRUE)))
    tfit <- vglm(y ~ 1, topple, data = tdata, trace = TRUE, crit = "coef")
    coef(tfit, matrix = TRUE)
    Coef(tfit)

[Package VGAM version 1.0-3 Index]