Question

Let X1,...,Xn i.i.d. Gamma(α,β) with α > 0, β > 0 (a) Assume both α and...

Let X1,...,Xn i.i.d. Gamma(α,β) with α > 0, β > 0
(a) Assume both α and β are unknown, find their momthod of moment estimators: αˆMOM and βˆMOM. (b) Assume α is known and β is unknown, find the maximum likelihood estimation for β.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
let X1, . . . , Xn i.i.d. Gamma(α, β), β > 0 known and α...
let X1, . . . , Xn i.i.d. Gamma(α, β), β > 0 known and α > 0 unknown. (a) Find the sufficient statistic for α (b) Use the sufficient statistic found in (a) to find the MVUE of α n . b) Use the sufficient statistic found in (a) to find the MVUE of α n
Let X1, X2, . . . Xn be iid random variables from a gamma distribution with...
Let X1, X2, . . . Xn be iid random variables from a gamma distribution with unknown α and unknown β. Find the method of moments estimators for α and β
Let X1, ..., Xn be a random sample from a probability density function: f(x; β) =...
Let X1, ..., Xn be a random sample from a probability density function: f(x; β) = βxβ−1 for 0 < x < 1 (where β > 0). a) Obtain the moment estimator for β. b) Obtain the maximum likelihood estimator for β. c) Is each of the estimators of a) and b) a sufficient statistic?
Let X1, X2, . . . , Xn be iid exponential random variables with unknown mean...
Let X1, X2, . . . , Xn be iid exponential random variables with unknown mean β. (1) Find the maximum likelihood estimator of β. (2) Determine whether the maximum likelihood estimator is unbiased for β. (3) Find the mean squared error of the maximum likelihood estimator of β. (4) Find the Cramer-Rao lower bound for the variances of unbiased estimators of β. (5) What is the UMVUE (uniformly minimum variance unbiased estimator) of β? What is your reason? (6)...
Let X1. ..., Xn, be a random sample from Exponential(β) with pdf f(x) = 1/β(e^(-x/β)) I(0,...
Let X1. ..., Xn, be a random sample from Exponential(β) with pdf f(x) = 1/β(e^(-x/β)) I(0, ∞)(x), B > 0 where β is an unknown parameter. Find the UMVUE of β^2.
4. Let X1. ..., Xn, be a random sample from Exponential(β) with pdf f(x) = 1/β(e^(-x/β))...
4. Let X1. ..., Xn, be a random sample from Exponential(β) with pdf f(x) = 1/β(e^(-x/β)) I(0, ∞)(x), B > 0 where β is an unknown parameter. Find the UMVUE of β2.
Let X1, ... , Xn be a sample of iid Gamma(?, 1) random variables with ?...
Let X1, ... , Xn be a sample of iid Gamma(?, 1) random variables with ? ∈ (0, ∞). a) Determine the likelihood function L(?). b) Use the Fisher–Neyman factorization theorem to determine a sufficient statistic S for ?.
Let X1, X2, · · · , Xn (n ≥ 30) be i.i.d observations from N(µ1,...
Let X1, X2, · · · , Xn (n ≥ 30) be i.i.d observations from N(µ1, σ12 ) and Y1, Y2, · · · , Yn be i.i.d observations from N(µ2, σ22 ). Also assume that X's and Y's are independent. Suppose that µ1, µ2, σ12 , σ22  are unknown. Find an approximate 95% confidence interval for (µ1µ2).
Let B > 0 and let X1 , X2 , … , Xn be a random...
Let B > 0 and let X1 , X2 , … , Xn be a random sample from the distribution with probability density function. f( x ; B ) = β/ (1 +x)^ (B+1), x > 0, zero otherwise. (i) Obtain the maximum likelihood estimator for B, β ˆ . (ii) Suppose n = 5, and x 1 = 0.3, x 2 = 0.4, x 3 = 1.0, x 4 = 2.0, x 5 = 4.0. Obtain the maximum likelihood...
Let X1, . . . , Xn be iid from a Poisson distribution with unknown λ....
Let X1, . . . , Xn be iid from a Poisson distribution with unknown λ. Following the Bayesian paradigm, suppose we assume the prior distribution for λ is Gamma(α, β). (a) Find the posterior distribution of λ. (b) Is Gamma a conjugate prior? Explain. (c) Use software or tables to provide a 95% credible interval for λ using the 2.5th percentile and 97.5th percentile in the case where xi = 13 and n=10, assuming α = 1 andβ =...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT