Different copula types and reliability applications for a new fisk probability model

In this research endeavor, the authors introduce a novel lifetime probability model. This distribution is meticulously examined and characterized, offering insights into its behavior and applicability in various contexts. The proposed new density function of this distribution has various heavy tail forms that are useful in the field of reliability, insurance and statistical modeling. This allows for the representation and modeling of a wide range of data sets that are diverse in their form and nature. The new distribution is characterized by having different patterns of risk or failure rates. The researchers extend the new distribution to the bivariate domain through different methods, including the Morgenstern-Farley-Gumbel distribution, the modified Morgenstern-Farley-Gumbel distribution, the famous Clayton mathematical versions, and the Rennie versions. These extensions enhance the usefulness of the proposed distribution in modeling multivariate age and reliability data and dependencies between variables. The study presents some statistical modeling experiments on reliability data and some important comparisons are presented within the framework of some statistical comparison criteria.