Homogeneous and Hybrid q-Mixture Forms of the Uma Distribution
Chapter from the book:
Tahtalı,
Y.
&
Demir,
İ.
&
Bayyurt,
L.
(eds.)
2025.
Current Approaches in Applied Statistics I.
Synopsis
Probability -distributions provide a flexible and dynamic framework that generalizes classical probability distributions by introducing the -parameter. This parameter allows for a broader class of probabilistic models, enriching both theoretical understanding and practical applications.
This study presents a comprehensive framework for the -analogues of the Uma distribution and provides an in-depth analysis of the specific cases corresponding to the homogeneous and hybrid types. Although these distributions exhibit similar probability density functions, they exhibit significant differences in terms of parameter constraints, generative mechanisms, and underlying statistical properties.
The study encompasses the modeling of the -analogues of both the probability density function and the cumulative distribution function, along with a detailed exploration of their shapes through rigorous mathematical analysis. Furthermore, the fundamental statistical and distributional characteristics of these distributions are thoroughly examined. Ultimately, these findings offer valuable insights for the continued exploration and application of -Uma distributions across various fields.
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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