Aims

Objectives

The following objectives will help you to assess how well you have mastered the relevant material. By the end of this section you should be able to:

• Write down the general form of the likelihood function and the log-likelihood function, based on a simple random sample from a distribution in a general parametric family.

• Define the maximium likelihood estimate(s) for one or more unknown parameters, based on a simple random sample from a distribution in a general parametric family.

• Write down the general form of the likelihood equations(s), based on a simple random sample from a distribution in a general parametric family, and understand how and when the maximum likelihood estimate(s) can be obtained from the solution of the likelihood equations(s).

• Find the explicit form of the likelihood equation(s) for a simple one- or two-parameter family of distributions, and solve to find the maximium likelihood estimate(s) of the unknown parameter(s).

• Find the maximum likelihood estimate directly from the likelihood function for a simple one-parameter range family.

• Compute the maximum likelihood estimate for population quantities which are simple functions of the unknown parameter(s). Examples of such functions include the population mean, the population median and the population variance, or appropriate poulation probabilities.

Suggested Reading

Handouts and Problem Sheets

Questions - set this week

PROBLEM SHEET 3 -- Questions 1, 3, 5

Interesting links