Invariant Exponential Models Applied to Reliability Theory and Survival Analysis

For a two-parameter exponential model with increasing failure rate (IFR) or decreasing failure rate (DFR) distributions necessary and sufficient conditions of the existence of a solution of the likelihood equations are given. Also, all of the scale-invariant two-parameter statistical models closed by raising to a power and by exponential tilting are introduced. The conditions of existence of a solution of the likelihood equations are studied for these invariant models, and the models are applied to obtain some uniformly most powerful unbiased tests of exponentially against alternatives in these models. © 1999 Taylor & Francis Group, LLC.