A MIXTURE OF EXPONENTIAL AND IFR GAMMA DISTRIBUTIONS HAVING AN UPSIDEDOWN BATHTUB-SHAPED FAILURE RATE

Abstract

We consider a mixture of one exponential distribution and one gamma distribution with increasing failure rate. For the right choice of parameters, it is shown that its failure rate has an upsidedown bathtub shape failure rate. We also consider a mixture of a family of exponentials and a family of gamma distributions and obtain a similar result.