
Explanation:
The correct answer is C.
The Fisher-Tippett theorem (also known as the Fisher-Tippett-Gnedenko theorem) is the fundamental theorem of Extreme Value Theory (EVT). It states that as the sample size gets large, the distribution of extremes (the maximum or minimum) of a sample of independent and identically distributed random variables converges to the Generalized Extreme Value (GEV) distribution. This is analogous to the Central Limit Theorem for sample means. Note that the Generalized Pareto Distribution (GPD) applies to the peaks-over-threshold (POT) approach, whereas the GEV applies to the block maxima approach.
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Q.4009 According to the Fisher-Tippett theorem, as the sample size n gets large, the distribution of extremes converges to:
A
a uniform distribution
B
a normal distribution
C
a generalized extreme value distribution
D
a generalized Pareto distribution
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