The two-parameter exponential. The cumulative distribution of the two-parameter exponential distribution can be written as
where µ is a location parameter and u is a scale parameter. Derive the best linear estimates of σ and µ using the first r order statistics Y,, ..., Y, from a sample of size n as follows.
(a) Give a formula for the expectation of k: in terms of that for a standard exponential distribution.
(b) Give a formula for the variance of I: in terms of that for a standard exponential distribution
(c) Give a formula for the covariance of and in terms of that for a standard exponential distribution.
For 11-3 and r=2:
(d) Numerically calculate the coefficients for the BLUES µ and σ*.
(e) Numerically calculate the factors for Var(µ*), Var( σ*), and 