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Sarthak Bagaria
SI 402: Statistical Inference

Project 1

Maximum Likelihood Estimation of the Gamma Shape

SI 402 Statistical Inference · Fall 2012 · Prof. Siuli Mukhopadhyay

Let X1, ..., Xn be a random sample from a Gamma(α, 1) distribution, α > 0. Find the maximum likelihood estimator (MLE) for α.

  1. Take n = 50. Suppose the true value of α = α0. You can choose your own α0. Generate a random sample from the Gamma(α0, 1) distribution. Remember that you actually do not know α0 but you are trying to estimate α based on the data you have generated. The procedure of generating the sample should be described briefly with proper references.

  2. Based on the sample determine the MLE of α. [Help: If you are using a numerical method which requires an initial value then you may use the value of the method of moment estimator for a starting value of α.] Describe the method used to find the MLE.

  3. Study the effect of choice of n on the MLE of α. Summarize your results in form of tables. What can you say about the effect of n on the MLE?

  4. Study the effect of changing the sample values on the estimate of α. For this question you can keep your n fixed at 50. Summarize your results.