fitweibull: Fit Four or Six Parametric Weibull Functions

In cardidates: Identification of Cardinal Dates in Ecological Time Series

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)

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.

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.

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.

Note

Note that the heuristics works optimal if unnecessary leading and trailing data are removed before the call.

Author(s)

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

Maintainer: Thomas Petzoldt <[e-mail]>

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, \Sexpr[results=rd]{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)

cardidates documentation built on Oct. 8, 2023, 1:06 a.m.