Let Y 1 , Y 2 , … , Y n denote a random sample of size n from a power family distribution (see Exercise 6.17). Then the methods of Section 6.7 imply that Y ( n ) = max( Y 1 , Y 2 , … , Y n ) has the distribution function given by F ( n ) = { 0 , y < 0 , ( y / θ ) α n , 0 ≤ y ≤ θ , 1 , y > θ . Use the method described in Exercise 9.26 to show that Y ( n ) is a consistent estimator of θ .
Let Y 1 , Y 2 , … , Y n denote a random sample of size n from a power family distribution (see Exercise 6.17). Then the methods of Section 6.7 imply that Y ( n ) = max( Y 1 , Y 2 , … , Y n ) has the distribution function given by F ( n ) = { 0 , y < 0 , ( y / θ ) α n , 0 ≤ y ≤ θ , 1 , y > θ . Use the method described in Exercise 9.26 to show that Y ( n ) is a consistent estimator of θ .
Solution Summary: The author explains the cumulative distribution function of Y_(n).
Let Y1, Y2, … , Yn denote a random sample of sizen from a power family distribution (see Exercise 6.17). Then the methods of Section 6.7 imply that Y(n) = max(Y1, Y2, … , Yn) has the distribution function given by
F
(
n
)
=
{
0
,
y
<
0
,
(
y
/
θ
)
α
n
,
0
≤
y
≤
θ
,
1
,
y
>
θ
.
Use the method described in Exercise 9.26 to show that Y(n) is a consistent estimator of θ.
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
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