1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Bayesian Statistics

  1. Mar 28, 2013 #1
    1. The problem statement, all variables and given/known data

    Let [itex]Y_n[/itex] be the nth order statistic of a random sample of size n from a distribution with pdf [itex]f(x|\theta) = 1/\theta[/itex], [itex]0<x<\theta[/itex], zero elsewhere. Take the loss function to be [itex]L[\theta, \delta(y)] = [\theta - \delta(y_n)]^2[/itex]. Let [itex]\theta[/itex] be an observed value of the random variable [itex]\Theta[/itex], which ahs the prior pdf [itex]h(\theta) = \beta\alpha^{\beta}/\theta^{\beta+1}[/itex], [itex]\alpha < \theta < \infty[/itex], zero elsewhere, with [itex]\alpha > 0[/itex], [itex]\beta > 0[/itex]. Find hte Bayes solution [itex]\delta(y_n)[/itex] for a point estimate of [itex]\theta[/itex].

    2. Relevant equations

    3. The attempt at a solution

    I'm a little confused with finding the likelihood function. Since they are telling us that [itex]Y_n[/itex] is the nth statistic...does that mean that we only have one function in the likelihood function?

    Thanks in advance
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted