Question: Consider the following method of estimating lambda for a Poisson distribution. Observe that p 0 = P(X=0) = e^(-lambda) Letting Y denote the number the

Consider the following method of estimating lambda for a Poisson distribution.

Observe that p₀= P(X=0) = e^(-lambda)

Letting Y denote the number the number of zeros from i.i.d. sample of size n, lambda might be estimated by

lambda_hat = -log(Y/n)

Use the method of propagation of error to obtain approximate expressions for the variance and the bias of this estimate. Compare the variance of this estimate to the variance of the mle, computing relative efficiencies for various values of lambda. Note that Y ~ bin( n , p₀).

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

rr1 all questions should be answered correctly SECTION C 9 Foundations of Functional Programming Consider binary trees that are either empty (written Lf) or have the form Br x t1 t2 where t1 and t2...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

\fCHAPTER 14 Server Farms: M/M/k and M/M/k/k In today's high-volume world, almost no websites, compute centers, or call centers consist of just a single server. Instead a \"server farm\" is used. The...

Submitted to Management Science manuscript MS-0001-1922.65 Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title....

Hi, it's me again Thanks for helping me with the answer last time d u 1. (a) Let Y1, Y2, ..., Yn be a random sample from a Bernoulli (p) distribution (i.e. Binomial(1, p)). Show ELI K is a minimal...

s1 educated (SSE) student for every three public school educated (PSE) students. Reasoning that students are not very dissimilar from threads, he suggests the following entry and exit routines be...

nodes, but at least its bias can be quantified by Markov Chain L. INTRODUCTION analysis and thus can be corrected via appropriate re-weighting The popularity of online social networks (OSNs) in...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

question; Question 5. Point allocation: (a) 25%; (b) 25%; (c) 25%; (d) 25% Suppose that the solution of a representative agent's portfolio allocation problem is given by the following Euler equation...

Two particles of masses m and 2m and charges q and 2q are thrown in uniform magnetic field such that both the particles move in circle of equal radii. Ratio of average power radiated by the first to...

Illustrate the strength and weakness of k-means in comparison with k-medoids?

A garage is reducing the prices of cars. Calculate the new prices. Model Old price ($) Decrease (%) Absolute change ($) New price ($) 15800 Ace 2.0 Beta 21 300 12.0 Carro 24200 0.5

A company sells a plant asset which originally cost $372000 for $120000 on December 31, 2018. The Accumulated Depreciation account had a balance of $142000 after the current year's depreciation of...