Show that exxgtk kalphaalpha - 1 for k large enough, Basic Statistics

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Show that exxgtk kalphaalpha - 1 for k large enough

When a cdf F(x) has a tail power of α (i.e., when 1 - F(x) ∝ x^-α for x large enough):

a. Show that E[X|X>K] = Kα/(α - 1) for K large enough. Discuss the existence of this expectation as a function of α.

b. Derive an estimate of E[X|X>K] based on a sample from F.

c. Evaluate the stability of this estimate as a function of K when F is a Pareto P(2), P(3), P(4) distribution.

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Basic Statistics: Show that exxgtk kalphaalpha - 1 for k large enough

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Basic Statistics: Show that exxgtk kalphaalpha - 1 for k large enough

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