weibull6 {cardidates} R Documentation

## Six-Parametric Weibull Function

### Description

Six-parametric Weibull function and its definite integral.

### Usage

```fweibull6(x, p)

aweibull6(p, lower = 0, upper = 365)
```

### Arguments

 `x` vector of function arguments `p` vector of function parameters with: `p` determines the offset before increase ofs = (p+1) * (1-p), `p` inflexion point of increasing branch, `p` steepness of increasing branch, `p` offset after the peak, `p` inflexion point of decreasing branch, `p` steepness of decreasing branch, `lower` lower limit of the cumulative (integrated) function, `upper` upper limit of the cumulative (integrated) function.

### Details

The six-parametric Weibull function is more flexible than the four-parametric version. It is possible to have different offsets before and after the peak. The function can be given by:

f(x) = (p4 + exp(-(x/p5)^p6)) (1-p1 * exp(-(x/p2)^p3))

for x ≥ 0.

### Value

`fweibull6` gives the function and `aweibull6` its definite integral (cumulative function or area under curve). Note that in contrast to `aweibull4`, the integral is solved numerically and that the function returns a scalar, not a vector.

### See Also

`weibull4`, `fitweibull`, `CDW`, `peakwindow`, `cardidates` `Vectorize`

### Examples

```x <- seq(0, 150)
plot(x, fweibull6(x, c(0.833, 40, 5, 0.2, 80, 5)), type = "l", ylim = c(0,2))

## interpretation of offsets
ofs1 <- 0.1
ofs2 <- 0.3
p1 <- 1-ofs1/(ofs2 + 1)

lines(x, fweibull6(x, c(p1, 20, 5, ofs2, 60, 5)), col = "red")

## definite integratel from zero to 150, returns scalar
aweibull6(c(p1, 20, 5, ofs2, 60, 5), lower = 0, upper = 150)

## use Vectorize to create vectorized functions
vec.aweibull6 <- Vectorize(aweibull6, "upper")
plot(x, vec.aweibull6(c(p1, 20, 5, ofs2, 60, 5), lower = 0, upper = x))
```

[Package cardidates version 0.4.8 Index]