Question

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 estimate for B, β ˆ

(iii) Obtain a method of moments estimator for B, β .

(iv) 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 a method of moments estimate for B, 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
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 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, 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)
Let X1, X2, . . . Xn be iid exponential random variables with unknown mean β....
Let X1, X2, . . . Xn be iid exponential random variables with unknown mean β. Find the method of moments estimator of β
6. Let θ > 1 and let X1, X2, ..., Xn be a random sample from...
6. Let θ > 1 and let X1, X2, ..., Xn be a random sample from the distribution with probability density function f(x; θ) = 1/(xlnθ) , 1 < x < θ. a) Obtain the maximum likelihood estimator of θ, ˆθ. b) Is ˆθ a consistent estimator of θ? Justify your answer.
Let X1, X2 · · · , Xn be a random sample from the distribution with...
Let X1, X2 · · · , Xn be a random sample from the distribution with PDF, f(x) = (θ + 1)x^θ , 0 < x < 1, θ > −1. Find an estimator for θ using the maximum likelihood
Let X1, X2, · · · , Xn be a random sample from the distribution, f(x;...
Let X1, X2, · · · , Xn be a random sample from the distribution, f(x; θ) = (θ + 1)x^ −θ−2 , x > 1, θ > 0. Find the maximum likelihood estimator of θ based on a random sample of size n above
1. Let X1, X2, . . . , Xn be a random sample from a distribution...
1. Let X1, X2, . . . , Xn be a random sample from a distribution with pdf f(x, θ) = 1 3θ 4 x 3 e −x/θ , where 0 < x < ∞ and 0 < θ < ∞. Find the maximum likelihood estimator of ˆθ.
Let X1,...,Xn be a random sample from the pdf f(x;θ) = θx^(θ−1) , 0 ≤ x...
Let X1,...,Xn be a random sample from the pdf f(x;θ) = θx^(θ−1) , 0 ≤ x ≤ 1 , 0 < θ < ∞ Find the method of moments estimator of θ.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT