CDW {cardidates}

Cardinal Dates Using Fitted Weibull Curves

Description

CDW (cardinal dates using Weibull curves) extracts “cardinal dates” from fitted four- and six-parametric Weibull curves.

Usage

CDW(p, xmin = 0, xmax = 365, quantile = 0.05, symmetric = FALSE)

CDWa(p, xmin = 0, xmax = 365, quantile = 0.05, symmetric = FALSE)

Arguments

p

object of class cardiFit returned by fitweibull6 or fitweibull4 or parameter vector of the fitted Weibull function,

xmin

left boundary (in day of year) of the integral under the curve,

xmax

right boundary (in day of year) of the integral under the curve,

quantile

two-sided quantile (percentage of integral) which defines beginning and end of the peak,

symmetric

if (TRUE), quantiles are calculated for the whole area under the curve, otherwise for each of the branches separately.

Details

CDW is a numerically improved version of the algorithm described in Rolinski et al. (2007). Version CDWa is an alternative, simplified version which sets the baseline before and after the peak to zero using appropriate offset parameters p[1] and p[4]. The original method described by Rolinski et al. 2007 (here called CDW) shifts the function for the left and right branch separately in the asymmetric case.

Value

A list with components:

x

x values of cardinal dates tMid, tBegin, tEnd,

y

the corresponding y values (divided by ymax),

p

parameters of the fitted Weibull function

See Also

weibull4, weibull6, fitweibull, peakwindow, metaCDW, 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

## identify cardinal dates from fitted curves
(smd  <- CDW(p))
(smda <- CDW(p, symmetric = FALSE))

## plot data, curve and cardinal dates
plot(x, y, ylim=c(0, 10), xlim = c(0, 365))
lines(o$x, o$f * f)
points(x, fweibull6(x, p) * f, col = "green")
points(smd$x, fweibull6(smd$x, p) * f, col = "orange", pch = 16)
points(smda$x, fweibull6(smda$x, p) * f, col = "red", pch = 1, cex = 1.2)

## for comparison: additional fit of a 4 parameter Weibull
res4  <- fitweibull4(x, y)
res4$r2
p <- res4$p
o <- res4$fit
f <- res4$ymax
smd  <- CDW(p)
lines(o$x, o$f * f, col = "blue")
points(smd$x, fweibull4(smd$x, p) * f, col = "blue", pch = 16)