MOMENTS OF GENERALIZED ORDER STATISTICS FROM DOUBLY TRUNCATED MODIFIED MAKEHAM DISTRIBUTION AND ITS CHARACTERIZAION

The Makeham distribution has been extensively used in modeling actuarial data and helps as a fundamental life distribution. It describes a mortality failure law in which the hazard rate is composed of two components: a non-aging failure distribution and an aging failure distribution, the latter characterized by an exponentially increasing failure rate. The concept of generalized order statistics (gos), introduced by Kamps in 1995, provides a unified model for combining several models of ordered random variables, including order statistics, record values, progressive type II right-censored order statistics and more. The development of recurrence relations for the moments of gos is an important field of research due to the model’s accessibility and flexibility. These recurrence relations simplify the computation of higher-order moments and establish the associations between moments of different orders. In this article, we have derived the recurrence relations of gos for single and product moments from the doubly truncated modified Makeham distribution and have also reduced these relations for specific ordered random schemes, such as order statistics, k−th record values and sequential order statistics for selected different values of parameters. In the final section, we have presented a characterization theorem based on the recurrence relations of the moments. This theorem has identified the doubly truncated modified Makeham distribution through its moment structure within the gos framework. This shows how important these relationships are for setting this distribution apart from other probability models.