Derive the cdf of the smallest order statistic


Complete the following:

Q: Consider a random sample of size n from a distribution with CDF (cumulative distribution function) F(x)=1-1/x if , and zero otherwise.

a) Derive the CDF of the smallest order statistic, X(1n)

b) Find the limiting distribution of X(1n)

c) Find the limiting distribution of Xn(1n)

Consider the CDF above. Find the limiting extreme-value distribution of and compare this result

 

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Basic Statistics: Derive the cdf of the smallest order statistic
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