Structural and Statistical Analysis of Finite Mixture Models Based on q-Calculus
Chapter from the book:
Tahtalı,
Y.
&
Demir,
İ.
&
Bayyurt,
L.
(eds.)
2025.
Current Approaches in Applied Statistics I.
Synopsis
The foundations of -analysis date back to the 1740s, when Euler introduced the theory of partitions, also referred to as additive analytic number theory. Over the years, the discovery of -calculus applications in fields such as operator theory, combinatory, probability theory, and many others has sparked tremendous interest in this mathematical framework.
Mixture distributions are probabilistic models in which a data set is assumed to originate from multiple underlying distributions, each contributing with a certain probability. These distributions are commonly used to model complex data structures more accurately.
This paper introduces -finite mixture models as a novel extension of the classical finite mixture family, motivated by recent progress in -calculus and generalized probability distributions. By incorporating a deformation parameter , the proposed mixture models offer enhanced modeling flexibility for a variety of stochastic phenomena. The fundamental distributional and statistical properties of the suggested -mixture models are systematically are explored.
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Copyright (c) 2025 Yalçın Tahtalı- İbrahim Demir- Lütfi Bayyurt; Ahmet Arvas- Mercan Hatipoğlu- Bahri Tokmak- Ömer Ugur- Berra Kocakoç- Gülistan Erdal- Beyhan Doğan- Dursun Yılmaz- Cem Gül- Bilge Gözener- Mehmet Can Kaya- Dursun Yılmaz- Feridun Taşdan- Rukiye Dağalp- Melike Tekin- Gülistan Erdal- Mustafa Talip Koyuncu- Burak Demir- Muhammet Fatih Aslan- Akif Durdu- Nurgül Okur- Tuğçe Yıldırım Dal- Uğur Ayık- Hasan Hüseyin Gül