Question

Let X have a gamma distribution with  and  which is unknown. Let  be a random sample from this distribution....

  1. Let X have a gamma distribution with  and  which is unknown. Let  be a random sample from this distribution.

(1.1) Find a consistent estimator for  using the method-of-moments.

(1.2) Find the MLE of  denoted by .

(1.3) Find the asymptotic variance of the MLE, i.e.

(1.4) Find a sufficient statistic for .

(1.5) Find MVUE for .

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
Suppose that you have a random sample of sizenfrom a population with Gamma density with α=...
Suppose that you have a random sample of sizenfrom a population with Gamma density with α= 3 but unknown β. Write down the likelihood function, and find a sufficient statistic. Find the MLE and the MOM estimators forβ. (Hint: They should be equal.) Then find the MSE for this estimator by finding the bias and the variance.Is it consistent? Is it MVUE? Explain why or why not.
Let X1,..., Xn be a random sample from a distribution with pdf as follows: fX(x) =...
Let X1,..., Xn be a random sample from a distribution with pdf as follows: fX(x) = e^-(x-θ) , x > θ 0 otherwise. Find the sufficient statistic for θ. Find the maximum likelihood estimator of θ. Find the MVUE of θ,θˆ Is θˆ a consistent estimator of θ?
Let Y1, Y2, . . ., Yn be a random sample from a Laplace distribution with...
Let Y1, Y2, . . ., Yn be a random sample from a Laplace distribution with density function f(y|θ) = (1/2θ)e-|y|/θ for -∞ < y < ∞ where θ > 0. The first two moments of the distribution are E(Y) = 0 and E(Y2) = 2θ2. a) Find the likelihood function of the sample. b) What is a sufficient statistic for θ? c) Find the maximum likelihood estimator of θ. d) Find the maximum likelihood estimator of the standard deviation...
Let Xl, n be a random sample from a gamma distribution with parameters a = 2...
Let Xl, n be a random sample from a gamma distribution with parameters a = 2 and p = 20.      a)         Find an estimator , using the method of maximum likelihood b) Is the estimator obtained in part a) is unbiased and consistent estimator for the parameter 0? c) Using the factorization theorem, show that the estimator found in part a) is a sufficient estimator of 0.
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
6. Let X1, X2, ..., Xn be a random sample of a random variable X from...
6. Let X1, X2, ..., Xn be a random sample of a random variable X from a distribution with density f (x)  ( 1)x 0 ≤ x ≤ 1 where θ > -1. Obtain, a) Method of Moments Estimator (MME) of parameter θ. b) Maximum Likelihood Estimator (MLE) of parameter θ. c) A random sample of size 5 yields data x1 = 0.92, x2 = 0.7, x3 = 0.65, x4 = 0.4 and x5 = 0.75. Compute ML Estimate...
Let X1, . . . , Xn be a random sample from a Poisson distribution. (a)...
Let X1, . . . , Xn be a random sample from a Poisson distribution. (a) Prove that Pn i=1 Xi is a sufficient statistic for λ. (b) The MLE for λ in a Poisson distribution is X. Use this fact and the result of part (a) to argue that the MLE is also a sufficient statistic for λ.
Let X1, . . . , Xn be a random sample from a Bernoulli(θ) distribution, θ...
Let X1, . . . , Xn be a random sample from a Bernoulli(θ) distribution, θ ∈ [0, 1]. Find the MLE of the odds ratio, defined by θ/(1 − θ) and derive its asymptotic distribution.
Let X1, X2,..., Xn be a random sample from a population with probability density function f(x)...
Let X1, X2,..., Xn be a random sample from a population with probability density function f(x) = theta(1-x)^(theta-1), where 0<x<1, where theta is a positive unknown parameter a) Find the method of moments estimator of theta b) Find the maximum likelihood estimator of theta c) Show that the log likelihood function is maximized at theta(hat)
Suppose that X follows a gamma distribution where alpha=2 but theta is unknown with the following...
Suppose that X follows a gamma distribution where alpha=2 but theta is unknown with the following observed values 50 100 200 300 1000 1) Find the sample mean of X 2) Find the MLE of theta
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT