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Reading 10b: Maximum Likelihood Estimates

Maximum Likelihood EstimatesClass 10, Orloff and Jonathan Bloom1 Learning Goals1. Be able to define the Likelihood function for a parametric model given Be able to compute the Maximum Likelihood estimate of unknown parameter(s).2 IntroductionSuppose we know we have data consisting of valuesx1,..,xndrawn from an exponentialdistribution. The question remains: which exponential distribution?!We have casually referred totheexponential distribution orthebinomial distribution orthenormal distribution. In fact the exponential distribution exp( ) is not a single distributionbut rather a one-parameter family of distributions.

Suppose that the lifetime of Badger brand light bulbs is modeled by an exponential distri-bution with (unknown) parameter . We test 5 bulbs and nd they have lifetimes of 2, 3, 1, 3, and 4 years, respectively. What is the MLE for ? answer: We need to be careful with our notation. With ve di erent values it is best to

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