On testing alternative classes of life distribution with guaranteed survival times

Nonparametric procedures are proposed for testing exponentiality against several new aging classes of life distributions. The main idea is to test if the lifetime of a system, whose failure time has occurred in between visits, belongs to some alternative new aging classes of life distribution. This knowledge enables us to better estimate premium amounts for clients by more accurately estimating value when encountering left or interval-censored data. One possible approach to perform these tests is based on the empirical distribution function. The limiting distributions of the presented test statistics are given for a well known alternative when the null distribution is exponential. For small sample sizes, the power of the tests are calculated. The results derived by a Monte Carlo method show an excellent power of these procedures for some common alternative distributions.