Purchase Solution

Poisson Sufficiency and Unbiased Estimators

Not what you're looking for?

Ask Custom Question

From a Poisson (θ) distribution a random sample X1, X2, ... , Xn is selected. Given that that S = X1 + ... + Xn is sufficient for θ and also has the Poisson(nθ) distribution, we can define gr,k(s) by
gr,k(s) = {s!/(s - r)!} n-r {1 - (k/n)}s-r, s = r, r + 1, ... , 0 otherwise,

in which r = 0, 1, 2, ...
and k is a real constant.

(i) Show that E[gr,k(S)] = θ^r exp(- kθ) = τr,k(θ).

Attachments
Purchase this Solution
Solution Summary

The solution contains the determination of a sufficient statistic for a Poisson parameter and obtaining an unbiased estimator for a function of the parameter.

Purchase this Solution
Free BrainMass Quizzes
Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

View More Free Quizzes
Related BrainMass Solutions

  • Distribution Theory - Estimation

    The moment and maximum likelihood estimation of the parameters of a Rayleigh density are discussed in the solution. The examination of unbiasedness, consistency, sufficiency of the proposed estimators are also discussed.

  • Max Likelihood Methods (Estimators)

    Find the maximum likelihood estimators for theta and rho. Are these two unbiased estimators? Please see attachment. 6.4.5 Let Y1

  • Mean and Variances, Estimates, Unbiased Property and Consistency

    595495 Mean and Variances, Estimates, Unbiased Property and Consistency Please see the attachment for probability questions. Find the means and variances of these estimators.

  • Unbiased estimators

    (a) Note that and are unbiased estimators of . Namely, . Hence, . Hence, for any values of m, n and , is an unbiased estimators of .

  • Point Estimation and Unbiased Estimators

    164454 Algebra: Point Estimation and Unbiased Estimators Please help with the following problems involving point estimation and unbiased estimator. Please show each step of your solution. Thank you.

  • Point Estimation and Unbiased Estimators

    Point Estimation and Unbiased Estimators are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

  • Calculations with unbiased estimators

    This solution helps with calculations involving unbiased estimators.

  • LAMDA

    Let LAMDA denot the MLE of lamda and LAMDA(b)=X1 (a) Show that both LAMDA and LAMDA(b) are unbiased (b) Calculate the variances of LAMDA and LAMDA(b) (c) Are these estimators consistent? which is the better estimator? See attachment please.

  • Poisson distribution and unbiased estimator

    131271 Poisson distribution and unbiased estimator I'm stuck on this problem and I was wondering if someone could help me out. My initial guess is that if you set e^-cY equals to e^-theta => you'll get that e^-c(ntheta) = e^-theta => c = 1/n.

View More Related Solutions