On Some Results of Geometric Mixture Models

Shojaee, Omid

doi:10.22034/cas.2025.499008.1046

On Some Results of Geometric Mixture Models

Document Type : Original Article

Author

Omid Shojaee

Department of Statistics, Faculty of Science, University of Zabol, Zabol, Iran

https://doi.org/10.22034/cas.2025.499008.1046

Abstract

Over recent decades, numerous methodologies have been developed to address the heterogeneity within populations. These methodologies vary in their application to both parametric and semi-parametric models, which are crucial for a broad spectrum of uses in reliability and survival analysis. Research indicates that mixture distributions serve as an effective approach to representing population heterogeneity. This study delves into geometric mixture models for survival functions (or distribution functions), exploring their inherent properties and features. We discuss various stochastic and distributional aspects of these mixtures. Additionally, we establish some conditions for stochastic comparisons based on the usual stochastic order, hazard rate order, and reversed hazard rate order. Furthermore, we integrate our findings with prominent semi-parametric models in reliability theory, including the additive hazard rate model, the proportional hazard rate model, the accelerated lifetime model, and the proportional reversed hazard rate model, which serve as foundational models in our geometric mixtures. To corroborate our findings, we will demonstrate numerical examples.

Graphical Abstract