Let Ｙ_1 denote the minimum of a random sample of size n from a distribution that has pdf f(x)=exp(-(x-θ)), θ<x<∞.
Let Z_n=n(Y_1-θ).
Investigate the limiting distribution of Z_n.
機率論題目
2015-02-11 4:36 am
回答 (3)
2015-02-12 7:48 am
✔ 最佳答案
f(x) = exp(-(x-θ))Y(1) = min(X1,X2,...,Xn)
F(X) =∫(θ,X) exp(-(t-θ)) dt
= 1 - exp(-(X-θ))
fY(1) (x) = n*[1-(1-exp(-(x-θ)))]^(n-1) * exp(-(x-θ))
= n*exp(-n(x-θ)) , X>θ
Zn = n(Y(1) - θ)
Y(1) = Zn /n + θ
dY(1)/dZn = 1/n
f Zn(Z) = n * exp(-n(Z /n + θ - θ)) * |1/n|
= exp(-Z) , Z >0
2015-02-18 7:57 pm
謝謝老怪物大大
也謝謝慈信大大
沒想到你們的答案一致
只是我另一位有力人士提供的答案為
Zn～Exp(λ=1)
也謝謝慈信大大
沒想到你們的答案一致
只是我另一位有力人士提供的答案為
Zn～Exp(λ=1)
2015-02-11 8:09 pm
P[Z_n > z] = P[Y_1-θ > z/n] = P[X_i > θ+z/n, i=1,2,...,n]
= { P[X_1 > θ+z/n] }^n = { exp(-z/n) }^n = exp(-z), z > 0
= { P[X_1 > θ+z/n] }^n = { exp(-z/n) }^n = exp(-z), z > 0
收錄日期: 2021-04-11 21:00:02
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150210000016KK04688