Purchase Solution

Maximum Likelihood Estimation - Random Sample from a Gamma

Not what you're looking for?

Ask Custom Question

Please include full explanation - see the attached file.

5. Let X1, X2, ..., Xn represent a random sample from a Gamma (3, theta), theta > 0. Determine the maximum likelihood estimator (MLE) of theta.

Attachments
Purchase this Solution
Solution Summary

The solution describes the Maximum Likelihood Estimation of the parameter of a Gamma distribution.

Solution Preview

Please see the attachment for solution.

Let be a random sample of size n from a Gamma . Then

Then the likelihood function of the sample is

...

Purchase this Solution
Free BrainMass Quizzes
Measures of Central Tendency

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

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.

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.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

View More Free Quizzes
Related BrainMass Solutions

  • Maximum Likelihood Estimation

    279716 Maximum Likelihood Estimation Let the random samples x1, x2, x3,... xn drawn from normal distribution with known mean zero a. Construct the likelihood function b. Find the Nature Log of the likelihood function c.

  • Poisson distribution

    Q3: A random sample X1, X2, . . . , Xn of independent observations is taken from a Gamma distribution, whose density function is given by [see the attachment].

  • Point Estimation in Statistics

    42404 Point Estimation in Statistics 20. A random sample of n bike helmets manufactured by a certain company is selecrted. Let X = the number abong n that are flawed ... a. Derive the maximum likelihood estimator ... b. Is the estimator unbiased?

  • Likelihood Function, Maximum Likelihood Estimate (MLE)

    ,n be a random sample from a Poisson distribution with parameter . Find the maximum likelihood estimate of . 5. Let 1,2,....,n be a random sample from a population distribution with mean and variance 2. Let .

  • Mathematical Statistics Objective type

    . , Xn, be a random sample from a Normally distributed population with mean 9 and variance 92.

  • Rao- Blackwell Theorem

    Solution Let be a random sample of size m from . Now the likelihood function of the sample is , where is a function of and and is a function of sample only.

  • Distribution Theory - Estimation

    A density function sometimes used by engineers to model length of life of electronic components is the Rayleigh density, given by if 0 < y1 a random sample from a Rayleigh distribution. a.

  • Maximum likelihood and Fisher information

    315418 Maximum likelihood and Fisher information Suppose x(sub 1), x(sub 2), ..., x(sub n) is a random sample from a distribution with probability density f(x/Î?)=( 1 / (Î?+1)) e^(-x/(Î?+1) where x>0 and Î?> -1 A.

  • Likelihood Ratio Test

    Also since are i.i.d. as exponential distribution with parameter 1/σ, by the additive property of exponential random variables we have follows a Gamma distribution with parameter and 1/σ. Thus the p.d.f. of is given by , Let .

View More Related Solutions