The guaranteed exponential distribution has density function where λ, G > 0 are unspecified…

The guaranteed exponential distribution has density function

where λ, G > 0 are unspecified parameters. Let T ( 1 ),… , n) be the order statistic on a sample of size n.

are independent exponentials with failure rate λ and hence determine the joint distribution of U and T^y (c) Establish methods for exact interval estimation of λ and G. (The likelihood ratio statistic gives rise to simple pivotals for these parameters.)

(d) Apply these results to the group 1 data of Table 1.1. For this purpose, omit the censored data points.