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This lesson reviews point estimation from a frequentist perspective. Method of moments and maximum likelihood methods are reviewed. Following that is a discussion of decision theory, optimal…
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The two examples in this video illustrate how to show a family of distributions is complete. The first example uses the definition of complete. The second definition relies on the properties of…
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In data reduction, there are two key principles that play a role in ensuring the statistics being used are efficient in reducing the data and contain information that isn't misleading: those of…
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Two examples are provided that illustrate using the Factorization Theorem to find a sufficient statistic.
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An example to illustrate how to find the joint probability density function of a random sample from a gamma distribution using the result that the gamma family of distributions is an exponential…
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Example to show that the gamma family of PDFs is an exponential family
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An example to illustrate how to show the geometric(p) family of distributions is an exponential family.
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Many of the important distributions belong to a special class of distributions because their probability mass function (PMF) or probability density function (PDF) satisfies a specific mathematical…
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In this lesson, we briefly review the concept of sufficiency and quickly move to minimal sufficiency. Following this is a brief discussion of ancillary statistics. We then focus on complete…
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When a random sample is drawn, some summary of the values is usually computed. Any well-defined summary may be expressed mathematically as a function of an n-dimension vector. The domain of that…
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Exponential families are a large family of probability density functions (PDF) and probability mass functions (PMF) that share certain convenient and important mathematical properties that are…
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