cardidates (version 0.4.9)

fitweibull: Fit Four or Six Parametric Weibull Functions

Description

Fit a four- or six-parametric Weibull function to environmental data.

Usage

fitweibull6(x, y = NULL, p0 = NULL, linint = -1, maxit = 2000)
fitweibull4(x, y = NULL, p0 = c(0.1, 50, 5, 100), linint = -1, maxit = 1000)

Value

A list with components:

p

vector of fitted parameters,

ymax

maximum y value used for transformation,

r2

coefficient of determination between transformed and fitted y values,

fit

data frame with the following columns:

• x~data (original or interpolated) used for curve fitting,

• y~data (transformed-original or interpolated) used for curve fitting,

• f~estimated function values.

Arguments

x, y

the x (in day of year) and y coordinates of a set of points. Alternatively, a single argument x can be provided.

p0

initial parameters for optimization. In case of p0 = NA a heuristic algorithm to derive initial values is used for fitweibull6.

linint

control parameter to select interpolation behavior. Negative values (default) specify automatic selection heuristic, zero disables interpolation. A positive value is interpreted as mandatory interpolation time step.

maxit

maximum number of iterations passed to the optimisation functions.

Author

Susanne Rolinski (original algorithm) and Thomas Petzoldt (package).

Maintainer: Thomas Petzoldt <[e-mail]>

Details

Function fitweibull6 uses extensive heuristics to derive initial parameters for the optimization. It is intended to work with data which are defined over an interval between 0 and 365, e.g. environmental data and especially for plankton blooms. Please note that the function does internal transformation: $$y_{rel} = y_i / y_{max}$$

Note that additional data points are inserted between original measurements by linear interpolation with time step = 1 before curve fitting if the number of original data points is too low (currently n < 35). You can set linint = 0 to switch interpolation off.

fitweibull4 has only built-in heuristics for data interpolation but not for guessing initial parameters which must be supplied as vector p0 in the call.

References

Rolinski, S., Horn, H., Petzoldt, T., & Paul, L. (2007): Identification of cardinal dates in phytoplankton time series to enable the analysis of long-term trends. Oecologia 153, 997 - 1008, tools:::Rd_expr_doi("10.1007/s00442-007-0783-2").

See Also

weibull4, weibull6, CDW peakwindow, cardidates

Examples

## create some test data
set.seed(123)
x <- seq(0, 360, length = 20)
y <- abs(rnorm(20, mean = 1, sd = 0.1))
y[5:10] <- c(2, 4, 7, 3, 4, 2)

## fit Weibull function with 6 free parameters
res <- fitweibull6(x, y)

## show some properties
res$r2
p <- res$p
o <- res$fit
f <- res$ymax

## fit 6 parameter Weibull with user-provided start parameters

x <- seq(0, 150)
y <- fweibull6(x, c(0.8, 40, 5, 0.2, 80, 5)) + rnorm(x, sd = 0.1)
plot(x, y)
res <- fitweibull6(x, y, p0 = c(0, 40, 1, 1, 60, 0))
plot(res)