Suppose that X1, , Xn form a random sample from the beta distribution with parameters and Let (, ) be the vector parameter a Find the method of moments estimator for b Show that the method of moments estimator is not the M L E

Question: Suppose that X1, . . . , Xn form a random sample from the beta distribution with parameters and . Let = (,

Suppose that X1, . . . , Xn form a random sample from the beta with parameters α and β. Let θ = (α, β) be the vector parameter.
a. Find the method of moment’s estimator for θ.
b. Show that the method of moment’s estimator is not the M.L.E.

Step by Step Solution

★★★★★

3.39 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The means of X i and X 2 i are respectively and 1 1 W... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

602-M-S-P-E (942).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

A function y = f(x) is defined as follows: y = f(x) 1.0 1.025 1.049 1.072 Compute the values of dyldx and vidr at x =1.05. X 1.0 1.05 1.10 1.15 X 1.20 1.25 1.30 y = f(x) 1.095 1.118 1.140

Let X1,..., Xn be a random sample from the pdf f(x|) = x-2, 0

Let X1,..., Xn be a random sample from the pdf f(x|) = e-(x-) where -

Suppose that X1, . . . , Xn form a random sample from a beta distribution for which both parameters and are unknown. Show that the M.L.E.s of and satisfy the following equation: log i= 1

Suppose that X1, . . . , Xn form a random sample from the beta distribution with parameters and , where the value of is known and the value of is unknown ( > 0). Show that the following statistic...

Stats 120B Homework 4: Due Thursday, Feb. 11 1. Let X and Y be two i.i.d random variables following N (3, 1). (a) Find the distribution of 2X + Y using any method you like. (b) Find the distribution...

Suppose that X1, . . . , Xn form a random sample from a uniform distribution with the following p.d.f.: f(x|) = 1/ * I ( x 2),where > 0 is the unknown parameter of interest. (a) Whats the support of...

Suppose that X1, . . . , Xn form a random sample from the normal distribution with unknown mean and known variance 2. In this problem, you will prove the missing steps from the proof that there is...

Suppose that X1, . . . , Xn form a random sample from the Bernoulli distribution with unknown parameter p, and the prior p.d.f. of p is a positive and differentiable function over the interval 0

Suppose that X1, . . . , Xn form a random sample from an exponential distribution for which the value of the parameter is unknown ( > 0) and must be estimated by using the squared error loss...

Oil producers are interested in high strength nickel alloys that are strong and corrosion resistant. An experiment conducted in which yield strengths were compared for nickel alloy tensile specimens...

Show how you might synthesize each of the following from the compounds indicated and any other needed reagents: (a) (b) Succinylcholine bromide (see "The Chemistry of . . . Biologically Important...

Current Attempt in Progress Assume that Steve Corporation has a contractual debt outstanding. Steve has available two means of settlement: It can either make immediate payment of \ ( \ $ 1 , 5 5 0 ,...

. Which of the following statements are true? (a) A draft is always a check. (b) A check is always a draft. (c) A note must involve at least three people. (d) All of the above

Consider Case Study 4.2 on page 170. Suppose 18 specimens were used for each type of paint in an experiment and the actual difference in mean drying time, turned out to be 1.0. (a) Does this seem to...

For the data of Exercise 4.4, calculate the variance using the formula (a) Of form (4.2.1); (b) In Theorem 4.1. Exercise 4.4 According to ecology writer Jacqueline Killeen, phosphates contained in...

National security requires that defense technology be able to detect incoming projectiles or missiles. To make the defense system successful, multiple radar screens are required. Suppose that three...

Cooley landscaping needs to borrow $34,000 for a new front-end dirt loader. The bank is willing to loan the money at 9% interest for the next 5 years with annual, semiannual, quarterly or monthly...

Problem 7-6 Stock Valuation [LO 1] Suppose you know that a companys stock currently sells for $65.10 per share and the required return on the stock is 12 percent. You also know that the total return...

Monetary policy affects securities prices by affecting investors' required return increasing the federal deficit affecting firms' capacity to generate earnings