Maximum Likelihood Estimation
Maximum Likelihood Estimation (MLE) is an alternative method that most statisticians prefer. It finds the values of β and η that maximise the likelihood of obtaining β and η given the observed data. The likelihood function consists of the product of the pdfs written once for each data point, with the distribution parameters unknown. Evaluated in logarithms, this function has many terms and is quite complicated. With two parameters, the log likelihood is a three-dimensional surface shaped like a mountain. The top of the mountain locates the maximum likelihood values. The MLE values are the most likely to be the true values. When the data set to be analysed contains 100 or more failures and has either many suspensions or data that is dirty or deficient, MLE tends to be more accurate than median rank regression. However, engineers, who like to see data plotted, find MLE deficient because of its inability to provide a good graphic display.