New classes of improved confidence intervals for the scale parameter of a two-parameter exponential distribution

Two new classes of improved confidence intervals for the scale parameter σσ of a two-parameter exponential distribution E(μ,σ)E(μ,σ) with unknown location parameter μμ are constructed. The first one is a two-parameter class of smooth intervals Ia,bIa,b, for a⩾1a⩾1 and bb in a specified range, which have the same ratio of endpoints as the minimum ratio of endpoints interval I0I0 but greater coverage probability. Within this class, a subclass of generalized Bayes intervals is found which contains, in particular, the Brewster and Zidek-type interval IBZIBZ as a member. Another subclass of smooth intervals that improve the coverage probability for all parameter values is identified. The intervals of the second class, though non-smooth, have a very simple and explicit functional form. The Stein-type interval ISIS is a member of this class and is shown to be empirical Bayes. The construction extends Maruyama’s (1998) [8] point estimation technique to the interval estimation problem.