MLE for Lifetimes of Electronic Compnents

Examples of Maximum Likelihood Estimators in page 419

Lifetimes of Electronic Components

data <- c(3, 1.5, 2.1)

# Let's define likelihood function of exponential distribution
lklh.exp<- function(x, theta) theta*exp(-theta*x)
log.lklh.exp <- function(x, theta) {
            -sum(log(theta)-theta*x)
            }

By default optim searches for parameters, which minimise the function fn.

In order to find a maximium, all I have to do is change the sign of the function, hence -sum(…).

result <- optim(par = 0.5, log.lklh.exp, x = data)

one-dimensional optimization by Nelder-Mead is unreliable:
use "Brent" or optimize() directly

According to the warning message, I shoud use another optimisation algorithm, as I have a one dimensional problem - a single parameter. Thus, I follow the advise and get:

result <- optim(par = 2, log.lklh.exp, x = x, method = "Brent", lower = 0, upper = 3)
theta <- result$par
theta

[1] 0.4545455

It’s actually the same result.

Let’s compare the result to fitdistr, which uses maximum liklihood as well.

library(MASS)
fitdistr(data, "Exponential")

     rate   
  0.4545455 
 (0.2624319)

Let’s plot it

curve(theta*exp(-theta*x), from=0, to=15)