3. The Lévy distribution with parameter 0 > 0 is characterized by having the density f(x; 0) = - {√nter ex (b) 270x³ exp(-20), (a) Suppose we have samples x1,..., n from the Lévy distribution with parameter 0. Find the maximum likelihood esti- mator for 0. x > 0 x ≤ 0 1 Hint: 1 •9 Τη X1 k = 1/2 and X = 1/(20). Is your estimator from part (a) unbiased? are samples from a Gamma distribution with parameters

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3. The Lévy distribution with parameter 0> 0 is characterized by having the
density
2703 exp(-210),
f(x; 0) =
(b)
x > 0
x ≤ 0
(a)
Suppose we have samples x₁,...,n from the
Lévy distribution with parameter 0. Find the maximum likelihood esti-
mator for 0.
Is your estimator from part (a) unbiased?
Hint: 1
1 are samples from a Gamma distribution with parameters
X1
In
k = 1/2 and X = 1/(20).
Transcribed Image Text:3. The Lévy distribution with parameter 0> 0 is characterized by having the density 2703 exp(-210), f(x; 0) = (b) x > 0 x ≤ 0 (a) Suppose we have samples x₁,...,n from the Lévy distribution with parameter 0. Find the maximum likelihood esti- mator for 0. Is your estimator from part (a) unbiased? Hint: 1 1 are samples from a Gamma distribution with parameters X1 In k = 1/2 and X = 1/(20).
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