R nls Different Errors occur - r

Question

I'm new in R programming and I don't get a solution to an error which occurs when I use the nls Function.
I try to fit the data from an ecdf (values are extracted and saved in y) to this function model with four parameters:
fitsim <- nls(y ~ exp(-(((a-Abfluss)/(c*(Abfluss-b)))^d)),
start = list( a=max(Abfluss), b=min(Abfluss),
c=3, d=1))
When I start the nls Function these error occurs:
Error in numericDeriv(form[[3L]], names(ind), env) :
Fehlender Wert oder etwas Unendliches durch das Modell erzeugt
which means there is a missing value ore some value with infinity is generated through the model.
My vectors Abfluss and y have both the same lengths. Aim is to get the parameter estimation.
Maybe the problem is, that the model only works under this conditions:
c>0, d>0, b<=Abfluss<=a.
I try already the na.rm=True command. Then another error appears:
Error in model.frame.default(formula = ~y + Abfluss, na.rm = TRUE) :
Variablenlängen sind unterschiedlich (gefunden für '(na.rm)')
which means, the Length of variables are different.
I appreciative for every kind of help and advice.
For a better understanding I attach my whole code with whole data:
time<-c(1851:2013)
Abfluss<- c(4853,4214,5803,3430,4645,4485,3100,4797,4030,3590,5396,9864,3683,4485,4064,3420,5396,
4895,3931,4238,3790,3520,4263,5474,3790,4700,5109,4525,4007,6340,4993,6903,8160,3600,3480,3540,
3540,4565,3333,7764,
4755,7940,3112,3169,4435,5365,9422,3150,10500,4512,3790,4618,6126,3769,3704,
5938,5669,4552,5458,5854,4867,6057,4783,5753,5736,4618,6091,5820,5007,7984, 4435,
4645,7465,5820,5988,6022,4300,6062,3302,4877,4586,5275,4410,3174,4966,4939,4638,
5541,5760,6495,5435,4952,4912,6092,5182,5820,5129,6436,6648,3063,5550,5160,4400,
9600,6400,6380,6300,6180,6899,4360,5550,4580,3894,5277,7520,6780,5100,5430,4550,
6620,4050,4560,5290,6610,8560,4943,6940,4744,6650,5700,7440,6200,4597,3697,7300,
4644,5456,6302,3741,5398,9500,6296,5279,5923,6412,6559,6559,5891,5737,5010,5790,
10300,4150,4870,6740,7560,8010,5120,8170,7430, 7330,5900, 11150)
#EV4-Distribution
dEV4 <- function(x, a, b, c,d) {
m<-exp(-(((a-Abfluss)/(c*(Abfluss-b)))^d))
return(m)
}
#Simulation example
Sim<-dEV4(Abfluss,a=max(Abfluss),b=min(Abfluss), c=3, d=1)
dEV4cdf<-cbind(Abfluss,Sim)
#Empirical cdf
p = ecdf(Abfluss)
y<- p(Abfluss) #Extracting of cumulated probabilities
m<-cbind(Abfluss,y)
#plot EV4 and ecdf
plot(dEV4cdf, type="p",main="EV4")
plot(ecdf(Abfluss), add=T)
#Fitting EV4 nls
fitsim <- nls(y ~ exp(-(((a-Abfluss)/(c*(Abfluss-b)))^d)),
start = list( a=max(Abfluss), b=min(Abfluss),
c=3, d=1), na.rm=TRUE)

Answer 1

Do not use starting values that are on the boundary of the feasible region and try nlxb in nlmrt instead (which can be used with the same arguments except data = is not optional):
library(nlmrt)
fitsim <- nlxb(y ~ exp(-(((a - Abfluss) / (c * (Abfluss - b))) ^ d)),
data = data.frame(y, Abfluss),
start = list(a = 2 * max(Abfluss), b = min(Abfluss) / 2, c = 3, d = 1))
plot(y ~ Abfluss, pch = 20)
o <- order(Abfluss)
fit <- y - fitsim$resid
lines(fit[o] ~ Abfluss[o], col = "red")
giving:
nlmrt class object: x
residual sumsquares = 0.02908 on 163 observations
after 5001 Jacobian and 6060 function evaluations
name coeff SE tstat pval gradient JSingval
a 20047.7 NA NA NA 1.119e-07 3251
b -1175384 NA NA NA 1.432e-09 0.1775
c 0.0129414 NA NA NA -0.1296 5.808e-06
d 12.146 NA NA NA -2.097e-06 6.798e-11