Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2018 • Question 6

Question

Math 6010 • Linear Models Spring 2018 • Question 6

Consider the density function \[ p(x;\alpha ,\lambda )=(2\pi x^3)^{-3/2} \exp \left \{(\alpha \lambda )^{1/2}-\frac {1}{2}\log \lambda -\frac {1}{2}\alpha x-\frac {\lambda }{2}x^{-1}\right \}, \qquad 0<x<\infty . \] Given \(X_1,X_2,\ldots ,X_n\) iid from this density find a sufficient statistic (that involves all of the \(X_i\)) for the parameters \((\alpha /2,\lambda /2)\).

Raw LaTeX

Consider the density function
\[
  p(x;\alpha,\lambda)=(2\pi x^3)^{-3/2}
  \exp\left\{(\alpha\lambda)^{1/2}-\frac{1}{2}\log\lambda
  -\frac{1}{2}\alpha x-\frac{\lambda}{2}x^{-1}\right\},
  \qquad 0<x<\infty.
\]
Given \(X_1,X_2,\ldots,X_n\) iid from this density find a sufficient statistic
(that involves all of the \(X_i\)) for the parameters \((\alpha/2,\lambda/2)\).

Topic Tags

Estimator Distributions Measure-Theoretic Probability Sufficiency, Completeness, and UMVUE Uniform Integrability and Truncation Methods