CAS Exam MAS-I Fall 2019, Question 33

Study guide: Exam MAS-I

You have a sample of five independent observations, x_1 \ldots x_5, each with exponential distribution:

f(x_i|\theta_i) = \frac{1}{\theta_i}\exp\left(-\frac{x_i}{\theta_i}\right)

• You are fitting this data to a model with \theta_i = \theta, for all i, using maximum likelihood estimation:

f(x_i|\theta) = \frac{1}{\theta}\exp\left(-\frac{x_i}{\theta}\right)

• The five observed values are: 100, 100, 500, 800, 1000
• The deviance of the model, D, is equal to twice the difference between the log-likelihood of the saturated model and the log-likelihood of the fitted model.

Calculate D.

• A) Less than 2
• B) At least 2, but less than 4
• C) At least 4, but less than 6
• D) At least 6, but less than 8
• E) At least 8

Answer this question and see the worked solution

Concepts tested

• Deviance
• Exponential Distribution
• Maximum Likelihood Estimation

More questions from this set

• CAS Exam MAS-I Fall 2019, Question 32
• CAS Exam MAS-I Fall 2019, Question 34