# weibull: Weibull equation (Weibull, 1951) In nlraa: Non-linear regression for agricultural applications

## Description

Weibull equation (Weibull, 1951). This is equation 2.4 in Table 1 of the paper referenced below.

## Usage

 `1` ```weibull(time, a, b, Yo) ```

## Arguments

 `time` a numeric vector of values at which to evaluate the model. `a` a and b paramaters define the shape of the response `b` a and b paramaters define the shape of the response `Yo` Yo is the max value for Y and when time is zero, Y is also zero

## Details

Applied to describe water stress index, crop N-uptake, seed germination, crop growth, LAI development, etc. Remark: a and b paramaters have not direct biological interperation and the unit of paramater a depends on paramater b and therefore is difficult to provide initial estimates for non-linear regression analysis. Usually the initial paramaters were provided by trial and error. But see SSweibull.

## Value

a numeric vector of length equal to the inputs

## Author(s)

Fernando E. Miguez

## References

Nonlinear Regression Models and Applications in Agricultural Research. Sotirios V. Archontoulis and Fernando E. Miguez. Agronomy Journal. doi: 10.2134/agronj2012.0506

`SSweibull`
 ```1 2 3 4 5 6 7 8``` ```require(lattice) ## Set parameter values and plot the relationship time <- seq(0, 200,5) ans1 <- weibull(time, a = 0.00025, b = 0.5, Yo=100) ans2 <- weibull(time, a = 0.00025, b = 1.5, Yo=100) ans3 <- weibull(time, a = 0.00025, b = 2, Yo=100) ans4 <- weibull(time, a = 0.00025, b = 3, Yo=100) xyplot(ans1 + ans2 + ans3 + ans4 ~ time, type="l", auto.key=TRUE, ylab = "text", xlab = "time") ```