weibull4 {cardidates} R Documentation

## Four-Parametric Weibull Function

### Description

Four-parametric Weibull function and its definite integral.

### Usage

```fweibull4(x, p)

aweibull4(p, lower, upper)
```

### Arguments

 `x` vector of function arguments, `p` vector of function parameters with: `p[1]` vertical shift (zero offset), `p[2]` vertical scaling, `p[3]` shape parameter a of `dweibull`, and `p[4]` scale parameter b of `dweibull`, `lower` lower limit of the cumulative (integrated) function, `upper` upper limit of the cumulative (integrated) function.

### Details

The four-parametric Weibull function is essentially based on the Weibull density function `dweibull` and its integral by the Weibull distribution function `pweibull` with two additional parameters for y scaling and zero offset. It can be given by:

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

for x ≥ 0.

### Value

`fweibull4` gives the Weibull function and `aweibull4` its definite integral (cumulative sum or area under curve).

`dweibull`, `weibull6`, `fitweibull`, `peakwindow`, `CDW`, `cardidates`

### Examples

```x <- seq(0, 5, 0.02)
plot(x, fweibull4(x, c(0, 1, 2, 1)), type = "l", ylim = c(0, 2))
points(x, dweibull(x, 2, 1), pch = "+") ## identical to former

## shape
lines(x, fweibull4(x, c(0, 2, 1.5, 1)), type = "l", col = "orange")
## horizontal scaling
lines(x, fweibull4(x, c(0, 2, 2, 2)), type = "l", col = "green")
## shifting
lines(x, fweibull4(x, c(1, 1, 2, 1)), type = "l", col = "blue")
## vertical scaling
lines(x, fweibull4(x, c(0, 2, 2, 1)), type = "l", col = "red")

## definite integral
p <- c(0, 1, 2, 2)
plot(x, aweibull4(p, lower = 0, upper = x))

p <- c(0.1, 1, 2, 2)
plot(x, aweibull4(p, lower = 0, upper = x))
```

[Package cardidates version 0.4.8 Index]