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

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/richards.R

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

1	weibull(time, a, b, Yo)

`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

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.

a numeric vector of length equal to the inputs

Fernando E. Miguez

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

SSweibull

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")