On some Asymptotic Properties of the Extended Cosine Burr XII Distribution

• DOI: 10.56919/usci.2434.031
• Publication Date: 2025-03-19T11:03:52Z
• Authors: Ibrahim Abdullahi; Usman Mukhtar; Isyaku Muhammad

Study’s Excerpt

The extended cosine Burr XII (ECSBXII) distribution model developed within the extended cosine-G family is introduced. The asymptotic properties of the mean residual life (MRL) and extreme order statistics specific to the ECSBXII distribution are derived. Practical application of the asymptotic MRL is shown using simulation studies.

Full Abstract In statistics, asymptotic functions provide a powerful framework for understanding the behavior of functions or statistical procedures within the limits of certain parameters. Also, in reliability, mean residual life assumes a critical role in evaluating the durability and effectiveness of diverse components. In addition, order statistics are essential tools in extreme value analysis. In this article, a new probability model is proposed based on the extended cosine-G family of distributions, called extended cosine Burr XII (ECSBXII) distribution. Some important basic properties are derived. We drive and study the asymptotic of mean residual life and asymptotic of the extreme order statistics of the ECSBXII distribution. An illustrative application of asymptotic MRL of ECBXII is given using simulation studies.