Lifetime Distributions and Equivalent Ages. Possible Applications in Insurance, Risk, and More

Boyan Dimitrov

In this Lecture we define age and comparable ages for individuals within one population or for objects from two (or more) different populations by making use of their lifetime distributions. The main purposes of this talk are not the proposed definitions, but the new look at the quantiles, and its relationships with other important probability characteristics. These definitions are all for equivalent ages, and may have different meaning important in applications. Respectively, there are various areas of use. All the other statements, as Corollaries, Theorems, and even the Examples are like consequences of the Definitions. For instance, as a consequence, we propose several ways for the evaluation of the true age of one individual on the background of his population. Also, a general approach to the time scaling in age evaluation in accelerated testing is offered, based on the accumulated total load. Then we generalize this definition to two-dimensional and multi-dimensional distributions that also may represent life times. Further we briefly sketch the areas where our method of equivalent age's and comparison can be applied.