?Hello,
I want to get the Maximum Likelihood Estimate (MLE) for an Extended weibull
with three parameters. I have two problems. First, some times if I change the
starting point for one of the parameters I got an error message. Second,
sometime when I change the starting point for one of the parameters the
solution changes. I don't know what I'm doing wrong or if there is a better way
to get the MLE for a distribution.
Here is my Example and the Error message.
Problem 1:
y=c(5,11,21,31,46,75,98,122,145,165,195,224,245,293,321,330,350,420) #My data
set
Nweibull <-
function(x,lambda,alpha,beta){lambda*beta*(x/alpha)^(beta-1)*exp(1)^((x/alpha)^beta+lambda*alpha*(1-exp(1)^((x/alpha)^beta)))}
# The PDF
LL <- function(lambda,alpha,beta) {
R = Nweibull(y,lambda,alpha,beta)
-sum(log(R))
} # defining the Likelihood Function
g=mle2(LL, start = list(lambda=.01,alpha=325,beta=.8),data = list(y),method =
"L-BFGS-B",lower=c(.00001,.00001,.00001),upper = c(Inf, Inf,Inf))
summary(g)
#### Out Put###
Maximum likelihood estimation
Call:
mle2(minuslogl = LL, start = list(lambda = 0.01, alpha = 325,
beta = 0.8), method = "L-BFGS-B", data = list(y), lower = c(1e-05,
1e-05, 1e-05), upper = c(Inf, Inf, Inf))
Coefficients:
Estimate Std. Error z value Pr(z)
lambda 3.6926e-03 8.9662e-04 4.1183e+00 3.817e-05 ***
alpha 3.2500e+02 1.1953e-04 2.7191e+06 < 2.2e-16 ***
beta 9.3856e-01 2.0186e-01 4.6496e+00 3.326e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
-2 log L: 218.7464
Now If I change the starting point for theta to be 0.7 I got the following
error message:
g=mle2(LL, start = list(lambda=.01,alpha=340,beta=.7),data = list(y),method =
"L-BFGS-B",lower=c(.00001,.00001,.00001),upper = c(Inf, Inf,Inf))
Error in optim(par = c(0.01, 325, 0.7), fn = function (p) :
L-BFGS-B needs finite values of 'fn'
Problem 2:
If I change the starting point for alpha to be 340 the optimal solution will
change too:
g=mle2(LL, start = list(lambda=.01,alpha=340,beta=.8),data = list(y),method =
"L-BFGS-B",lower=c(.00001,.00001,.00001),upper = c(Inf, Inf,Inf))
summary(g)
Maximum likelihood estimation
Call:
mle2(minuslogl = LL, start = list(lambda = 0.01, alpha = 340,
beta = 0.8), method = "L-BFGS-B", data = list(y), lower = c(1e-05,
1e-05, 1e-05), upper = c(Inf, Inf, Inf))
Coefficients:
Estimate Std. Error z value Pr(z)
lambda 3.7938e-03 9.3580e-04 4.0541e+00 5.034e-05 ***
alpha 3.4000e+02 1.2039e-04 2.8243e+06 < 2.2e-16 ***
beta 9.6164e-01 2.0766e-01 4.6309e+00 3.642e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
-2 log L: 218.7979
Thanks,
Mosab
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