Distribution Theory - Estimation
Not what you're looking for?
1. A density function sometimes used by engineers to model length of life of electronic components is the Rayleigh density, given by if 0 < y1 <infinity, 0 otherwise. Assume Y1, Y2, ...Yn is a random sample from a Rayleigh distribution.
a. If Y has the Rayleigh density, find the probability density for U = Y2.
b. Use part a to find E(Y) and V(Y).
c. Use the first moment E(Y) to find a method of moment estimator for .
d. Use the second moment E(Y) to find a method of moment estimator for .
e. Find the MLE of . Denote this as .
f. What is the asymptotic variance of ?
g. Show whether is an unbiased estimator for .
h. Show whether is a consistent estimator for .
i. Show whether is sufficient for .
Purchase this Solution
Solution Summary
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.
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.
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.
Measures of Central Tendency
Tests knowledge of the three main measures of central tendency, including some simple calculation questions.