A Hybrid Support Vector Machine–Genetic Algorithm Framework for Estimating the DUS-Transformed Generalized Polynomial Quadratic Failure Rate Distribution

Probability distributions are essential statistical instruments, which make it possible to model and analyze some probability events in various spheres, including engineering, medicine, finance, and environmental science. Classical distributions, however, have been observed to have constraints in describing the complexity of real-life data. This paper will discuss these shortcomings by proposing the DUS-transformed Generalized Polynomial Quadratic Failure Rate (DUS-GPQF) distribution, which is a new extension of the generalized linear failure rate (GLF) distribution via DUS transformation method. The DUS-GPQF distribution increases the flexibility in the GLF model which provides it with greater ability to support a larger spectrum of data behaviors. The DUS-GPQF distribution has important statistical properties which include the hazard rate functional, moments, incomplete moments, entropy and the extropy. The DUS-GPQF distribution has seventeen estimation methods, which guarantee that it is practical to apply. The tests on the DUS-GPQF distribution are performed on two real-world data sets, and the results show that the model is better than other competitive models in goodness of fit and predictive accuracy. The study offers a powerful statistical model to a complex data so as to improve theoretical as well as practical statistical analysis.