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Summary | 8 Annotations
the likelihood is a function that associates to each parameter the probability (or probability density) of observing the given sample
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a sample
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e ,
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realization of a random vector ,
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distribution of belongs to a parametric family: there is a set of real vectors (called the parameter space) whose elements (called parameters) are put into correspondence with the distributions that could have generated ;
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a function of for fixed (i.e., for the sample we have observed), it is called likelihood (or likelihood function) and it is denoted by .
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log-likelihood function is the function defined by
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by finding the parameter that maximizes the log-likelihood of the observed sample . This is the same as maximizing the likelihood function
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