Y1, Y2, ... Yn are a random sample from the Gamma distribution with parameters α and β

Question

Question

Y1, Y2, ... Yn are a random sample from the Gamma distribution with parameters α and β

(a) Suppose that α-4 is known and β is unknown. Find a complete sufficient statistic for β. Find the MVUE of β. (Hint: What is E(Y)?)

(b) Suppose that β = 4 is known and a is unknown. Find a complete sufficient statistic for α.

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Add a comment

Answer 2

Similar Homework Help Questions

with parameters α and β. 2. Yİ,%, , Y, are a random sample from the Gamma distribution (a) Suppose that α 4 is known and β is unknown. Find a complete sufficient statistic for β. Find the MVUE of β....

with parameters α and β. 2. Yİ,%, , Y, are a random sample from the Gamma distribution (a) Suppose that α 4 is known and β is unknown. Find a complete sufficient statistic for β. Find the MVUE of β. (Hint: What is E(Y)?) (b) Suppose that β 4 is known and α is unknown. Find a complete sufficient statistic for a. with parameters α and β. 2. Yİ,%, , Y, are a random sample from the Gamma distribution (a)...
Exercise: Let Yİ,Y2, ,, be a random sample from a Gamma distribution with parameters and β. Assum...

Exercise: Let Yİ,Y2, ,, be a random sample from a Gamma distribution with parameters and β. Assume α > 0 is known. a. Find the Maximum Likelihood Estimator for β. b. Show that the MLE is consistent for β. c. Find a sufficient statistic for β. d. Find a minimum variance unbiased estimator of β. e. Find a uniformly most powerful test for HO : β-2 vs. HA : β > 2. (Assume P(Type!Error)- 0.05, n 10 and a -...
. Suppose the Y1, Y2, · · · , Yn denote a random sample from a...

. Suppose the Y1, Y2, · · · , Yn denote a random sample from a population with Rayleigh distribution (Weibull distribution with parameters 2, θ) with density function f(y|θ) = 2y θ e −y 2/θ, θ > 0, y > 0 Consider the estimators ˆθ1 = Y(1) = min{Y1, Y2, · · · , Yn}, and ˆθ2 = 1 n Xn i=1 Y 2 i . ii) (10 points) Determine if ˆθ1 and ˆθ2 are unbiased estimators, and in...

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the distribution...

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the distribution having p.d.f f(x) = e-y , 0<y<, zero elsewhere. Answer the following questions. (a) decide whether Z1 = Y2 and Z2=Y4-Y2 are stochastically independent or not. (hint. first find the joint p.d.f. of Y2 and Y4) (b) show that Z1 = nY1, Z2= (n-1)(Y2-Y1), Z3=(n-2)(Y3-Y2), ...., Zn=Yn-Yn-1 are stocahstically independent and that each Zi has the exponential distribution.(hint use change of variable technique)
QUESTION 3 Let Y1, Y2, ..., Yn denote a random sample of size n from a...

QUESTION 3 Let Y1, Y2, ..., Yn denote a random sample of size n from a population whose density is given by (Parcto distribution). Consider the estimator β-Yu)-min(n, Y, where β is unknown (a) Derive the bias of the estimator β. (b) Derive the mean square error of B. , Yn).
Let X1 ,……, Xn be a random sample from a Gamma(α,β) distribution, α> 0; β> 0....

Let X1 ,……, Xn be a random sample from a Gamma(α,β) distribution, α> 0; β> 0. Show that T = (∑n i=1 Xi, ∏ n i=1 Xi) is complete and sufficient for (α, β).

Let Y1, Y2, . . . , Yn be independent random variables with Exponential distribution with...

Let Y1, Y2, . . . , Yn be independent random variables with Exponential distribution with mean β. Let Y(n) = max(Y1,Y2,...,Yn) and Y(1) = min(Y1,Y2,...,Yn). Find the probability P(Y(1) > y1,Y(n) < yn).
Let Y1,…,Yn~iid Gamma(5,β). Recall that Γ(5) = 4! a) Find the MLE for β. b) Is...

Let Y1,…,Yn~iid Gamma(5,β). Recall that Γ(5) = 4! a) Find the MLE for β. b) Is your answer to a) the MVUE? Use two methods to verify that it is unbiased.
Suppose Y1, Y2, Y3, Y4, Y5 is a random sample from a gamma distribution where the...

Suppose Y1, Y2, Y3, Y4, Y5 is a random sample from a gamma distribution where the shape parameter is known to be 2 and the scale parameter is unknown. a) Show that is a pivotal quantity. b) Show that is a pivotal quantity. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image

6.29. Let Xi, X2, , X,be a random sample from a gamma distribution with known parameter α-3 and unknown β > 0,' Discuss the construction of a confidence interval for B. Hint: what is the di...

6.29. Let Xi, X2, , X,be a random sample from a gamma distribution with known parameter α-3 and unknown β > 0,' Discuss the construction of a confidence interval for B. Hint: what is the distribution of 2 Σ x/P Follow the procedure outlined in Exercise 6.28. 6.29. Let Xi, X2, , X,be a random sample from a gamma distribution with known parameter α-3 and unknown β > 0,' Discuss the construction of a confidence interval for B. Hint: what...

Y1, Y2, ... Yn are a random sample from the Gamma distribution with parameters α and β

Homework Answers

Add Answer to:
Y1, Y2, ... Yn are a random sample from the Gamma distribution with parameters α and β

Post as a guest

Earn Coins

with parameters α and β. 2. Yİ,%, , Y, are a random sample from the Gamma distribution (a) Suppose that α 4 is known and β is unknown. Find a complete sufficient statistic for β. Find the MVUE of β....

Exercise: Let Yİ,Y2, ,, be a random sample from a Gamma distribution with parameters and β. Assum...

. Suppose the Y1, Y2, · · · , Yn denote a random sample from a...

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the distribution...

QUESTION 3 Let Y1, Y2, ..., Yn denote a random sample of size n from a...

Let X1 ,……, Xn be a random sample from a Gamma(α,β) distribution, α> 0; β> 0....

Let Y1, Y2, . . . , Yn be independent random variables with Exponential distribution with...

Let Y1,…,Yn~iid Gamma(5,β). Recall that Γ(5) = 4! a) Find the MLE for β. b) Is...

Suppose Y1, Y2, Y3, Y4, Y5 is a random sample from a gamma distribution where the...

6.29. Let Xi, X2, , X,be a random sample from a gamma distribution with known parameter α-3 and unknown β > 0,' Discuss the construction of a confidence interval for B. Hint: what is the di...

Y1, Y2, ... Yn are a random sample from the Gamma distribution with parameters α and β

Homework Answers

Add Answer to: Y1, Y2, ... Yn are a random sample from the Gamma distribution with parameters α and β

Post as a guest

Earn Coins

Add Answer to:
Y1, Y2, ... Yn are a random sample from the Gamma distribution with parameters α and β