# [R] R 3.1.2 mle2() function on Windows 7 Error and multiple optimal solutions

Mosab Alqurashi malqurashi at KSU.EDU.SA
Wed Jan 14 10:49:46 CET 2015

```?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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