EB lifetime distributions as alternative to the EP lifetime distributions

In this paper we consider lifetime distributions called EB-Max distribution and EB-Min. In the conditions of the Poisson’s Limit Theorem it is shown that EB-Max distribution may be approximated by its analogous called EP-Max lifetime distribution and EB-Min distribution may be approximated by its analogous EP-Min lifetime distribution. Further, as example, two methods are provided to simulate pseudo random number for EB-Min distribution and we apply EM algorithm to estimate parameters of EB-Min distribution. An example with real data is also presented and the proposed simulation algorithms where implemented in Maple.