Transcription of Reading 10b: Maximum Likelihood Estimates
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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. Each value of defines a different dis-tribution in the family, with pdff (x) = e xon [0, ). Similarly, a binomial distributionbin(n,p) is determined by the two parametersnandp, and a normal distributionN( , 2)is determined by the two parameters and 2(or equivalently, and ).]
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:
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