Question: In random sampling from the exponential distribution f (x) = (1/)ex/, x 0, > 0, find the maximum likelihood estimator of and

In random sampling from the exponential distribution f (x) = (1/θ)e−x/θ, x ≥ 0, θ > 0, find the maximum likelihood estimator of θ and obtain the asymptotic distribution of this estimator.

Step by Step Solution

★★★★★

3.42 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The loglikelihood is lnL nine 10 The maximum likelihood estimator is ob... 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)

3-M-E-E-A (122).docx

120 KBs Word File

Students Have Also Explored These Related Econometric Questions!

In random sampling from the exponential distribution f (x) = (1/)e x/ , x 0, > 0, find the maximum likelihood estimator of and obtain the asymptotic distribution of this estimator.

X is a random variable with an exponential distribution with parameter = .7 Thus the cdf of X is f(x) = .7 e.7 x for x 0. d) Calculate the probability that X > 6. Use the pexp function e) Calculate...

Random variables X and Y are independent exponential random variables with expected values E[X] = 1/ and E[Y] = 1/. If , what is the PDF of W = X + Y? If = what is fw(w)?

7.37 Let x1,..., xn be the observed values of a random sample of size n from the exponential distribution f (x; ) = 1ex/ for x > 0. (a) Find the maximum likelihood estimator of . (b) Obtain the...

10-39. Let X1, . . . ,Xn depict a random sample drawn from the exponential probability density function f (x; ) = 1 ex/ , x 0, > 0. Find an efficient or minimum variance unbiased estimator for...

Let $x_{1}, \ldots, x_{n}$ be the observed values of a random sample of size $n$ from the exponential distribution $f(x ; \beta)=\beta^{-1} e^{-x / \beta}$ for $x>0$. (a) Find the maximum...

6. A random sample X1, ..., Xn is taken from a Poisson distribution with mean 1, 1 > 0. a) Find the maximum likelihood estimator of 1. b) Let X be the number of flaws per 100 feet of a used computer...

3. The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution function 1 1 f(x) = x 20 lo, elswhere Find the...

Japanese firms and Chinese firms are competing in a single market. The cost function of a Japanese firm is TC 1 (Q)=8+2Q 2 and the cost function of a Chinese firm is TC 2 (Q)=16+Q 2 . Which of the...

Proctored Nonproctored H 12 n 30 33 78.23 81.15 S 11.63 18.41

Treat the two distributions below as populations. Calculate the variance for each distribution and present your answers with the appropriate symbol: First 12 13 11 11 9 a. Sample One: 7 b. Sample...

Auditors are required to establish an understanding with a nonprofit organization about the terms of the engagement in what way? A. Orally. O B. In the engagement workpapers. O c. In an engagement...

Instant messaging is a type of service. Time left 0 : 2 3 : 4 2 a . email b . network c . wireless d . chat e . cellular

Date: 16 JAN 2018 07:42:35 +0000 From: "Arnold Anderson" Subject: Apollo Shoes and Computers Darlene mentioned your inquiry earlier this week, and yes, Anderson, Olds, and...

Explain the relationship between bias, prejudice, stereotyping, and discrimination

Prove or disprove: There exist two connected graphs G and H both of order at least 3 and neither of which is Eulerian such that G + H is Eulerian.

Write two different techniques to declare and initialize a variable with an example.(reference:C++)

Write a program that simulates a simple calculator. It reads two integers and a character. If the character is a +, the sum is printed; if it is a -, the difference is printed; if it is a *, the...

Which of the following statements best describes how a single-name CDS contract is priced at inception? A. If the reference entitys credit spread trades below the standard coupon rate, the CDS...

We are interested in the ordered probit model. Our data consist of 250 observations, of which the responses are Using the preceding data, obtain maximum likelihood estimates of the unknown parameters...

For the zero-inflated Poisson (ZIP) model in Section 18.4.8, we derived the conditional mean function, E[y i |xi, w i ] = (1 F i ) i . a. For the same model, now obtain Var[yi |x i , w i ]. Then,...

Heteroskedastic fixed effects models. This is based on problem 96.5.1 in Econometric Theory by Baltagi (1996). Consider the fixed effects model \[y_{i t}=\alpha_{i}+u_{i t} \quad i=1,2, \ldots, N ;...

Bounds for $s^{2}$ in a one-way random effects model. For the random one-way error component model given in (2.1) and (2.2), consider the OLS estimator of \(\operatorname{var}\left(u_{i...

Prediction in the one-way random effects model. (a) For the predictor $y_{i, T+S}$ given in (2.37), compute $E\left(u_{i, T+S} u_{i t}ight)$ for $t=$ $1,2, \ldots, T$ and verify that...

Assume that your parents wanted to have $ 1 6 0 , 0 0 0 saved for university by your 1 8 th birthday and they started saving on your first birthday. They saved the same amount each year on your...