Razi University

  this dissertation, two novel probability distributions are introduced andcomprehensively investigated through a generalized approach based on theKumaraswamy-G-Poisson family. First, the six-parameterKumaraswamy-Fréchet-Poisson Distribution (KFPD) is derived by compounding theaforementioned family with the Fréchet distribution. Leveraging theheavy-tailed nature of the Fréchet distribution, this model exhibits a highcapability in modeling extreme-value and lifetime data with non-monotonichazard rate functions. Subsequently, the five-parameterKumaraswamy-Poisson-Gompertz Distribution (KPG) is proposed by replacing thebaseline distribution with the Gompertz distribution, which proves particularlyefficient for survival data characterized by exponential and increasing hazardrates.Thekey statistical properties of both models, including probability densityfunctions, cumulative distribution functions, reliability functions, hazardrate functions, probability-weighted moments, order statistics, quantilefunctions, and entropy measures, are rigorously derived and analyzed. Parameterestimation for both models is carried out via the Maximum Likelihood Estimation(MLE) method, and the performance of the estimators is evaluated throughextensive simulation studies. To assess practical applicability, bothdistributions are fitted to several real-world datasets from diverse fields,including medical, engineering, and financial data. The numerical results andcomparisons with well-known competing distributions indicate a satisfactoryfit, remarkable flexibility, and significant superiority of the proposed modelsin handling skewed, heavy-tailed, and complex hazard rate data. Overall, thefindings of this dissertation suggest that the KFPD and KPG distributions serveas powerful and generalized tools in lifetime and reliability data analysis,