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 ).]

We have casually referred to the exponential distribution or the binomial distribution or the normal distribution. In fact the exponential distribution exp( ) is not a single distribution but rather a one-parameter family of distributions. Each value of de nes a di erent dis-tribution in the family, with pdf f (x) = e x on [0;1). Similarly, a ...

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  Distribution, Maximum, Estimates, Exponential, Likelihood, Tribution, Exponential distribution, Maximum likelihood estimates

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