Document Details

Document Type : Thesis 
Document Title :
On a New Family of Distributions for Modeling Financial Data
حول عائلة جديدة من التوزيعات لنمذجة البيانات المالية اقتراح عائلة جديدة من التوزيعات
 
Subject : Faculty of Science 
Document Language : Arabic 
Abstract : The probability distributions are a very useful tool in several areas of engineering, science, economics, finance, etc. The random phenomenon in different studies is modeled by using a certain probability distribution. The ever-evolving complexities in data behavior have attracted a lot of researchers to develop new probability distributions. In recent years, some attention has been given to the development of the families of probability distributions. This has opened door to a vast area of research and various families of distributions have been proposed in the past decade. One limitation in the available families of distributions is that they used a [0, ∞) random variable as a generator and hence exclude the distributions whose domain begins with some constant 𝒂which is greater than 0. In this research a new inverse Kumaraswamy (NIK) distribution has been proposed which is defined on [1, ∞). The proposed distribution has been used to obtain a new family of distributions; named as the new inverse Kumaraswamy family of distributions (NIKFD). Some desirable properties of the proposed family of distributions have been explored. The proposed family of distributions has been studied for Weibull and Burr-XII baseline distributions giving rise to the new inverse Kumaraswamy-Weibull (NIKW) and the new inverse Kumaraswamy-Burr-XII (NIKB-XII) distributions. These distributions have been comprehensively explored and general properties; including moments, generating functions, hazard rate function, entropy, random number generation, etc.; are studied. The parameters of the proposed distributions have been estimated by using the maximum likelihood method with a random sample and with dual generalized order statistics. The Least square estimation of the parameters has also been done. An extensive simulation study has been conducted to see the performance of the estimates. The proposed distributions are used to model some real-life data and it has been found that the proposed distributions are suitable models for modeling the used data. The NIK distribution has also been explored, specifically, in the context of the dual generalized order statistics (DGOS). The distribution of single DGOS and joint distribution of two DGOS have been obtained. The moments of DGOS are also obtained alongside some recurrence relations to obtain the higher order moments from the corresponding lower order moments. The recurrence relations for special cases of DGOS have also been obtained. It is expected that the material contained in this thesis will open new doors of research for other graduate students. 
Supervisor : Prof. Muhammad Qaiser Shahbaz 
Thesis Type : Doctorate Thesis 
Publishing Year : 1444 AH
2023 AD 
Co-Supervisor : Prof. Bander Al-Zahrani 
Added Date : Thursday, April 27, 2023 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
عبدالقادر منير داغستانيDaghistani, Abdulkader MonierResearcherDoctorate 

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