Let X1, , Xn m be a random sample from the exponential distribution with parameter Suppose that has the gamma prior distribution with known parameters and Assume that we get to observe X1, , Xn, but Xn 1, , Xn m are censored a First, suppose that the censoring works as follows For i 1, , m, if Xn I...

a For each censored observation X ni we observe only that X ni c The probability of X ni c given is 1 expc The likelihood times prior is a constant ti ...

Let X1, . . . , Xn+m be a random sample from the exponential distribution with parameter

Question:

Let X1, . . . , Xn+m be a random sample from the exponential with parameter θ. Suppose that θ has the gamma prior with known parameters α and β. Assume that we get to observe X1, . . . , Xn, but Xn+1, . . . , Xn+m are censored.
a. First, suppose that the censoring works as follows: For i = 1, . . . , m, if Xn+I ≤ c, then we learn only that Xn+i ≤ c, but not the precise value of Xn+i. Set up a Gibbs sampling algorithm that will allow us to simulate the posterior of θ in spite of the censoring.
b. Next, suppose that the censoring works as follows: For i = 1, . . . , m, if Xn+i ≥ c, then we learn only that Xn+i ≥ c, but not the precise value of Xn+i. Set up a Gibbs sampling algorithm that will allow us to simulate the posterior of θ in spite of the censoring. Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...