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    An extension of the weibull distribution via alpha logarithmic g family with associated quantile regression modeling and applications
    (CRC Press, 2023) Akdoğan, Yunus; Karakaya, Kadir; Korkmaz, Mustafa Çağatay; Şahin, Fatih; Genç, Aşir
    In this paper, a novel lifetime model based on the Weibull distribution is presented. The new model is named the alpha logarithmic Weibull. The alpha logarithmic Weibull distribution has a decreasing, increasing and monotone hazard rate. Some distributional properties of the new model including the hazard rate function, moments, order statistics, and stochastic ordering are obtained. The new model includes some special sub-models and they are reported in detail. We examined five estimation methods which are maximum likelihood, Anderson-Darling, Cramer-von Mises least-squares and weighted least squares, to estimate three parameters of the new distribution. Extensive simulation studies are also conducted to observe the performance of the five estimators. Based on the new distribution, a new quantile regression model is also introduced. To estimate the parameters of a novel quantile regression model, the maximum likelihood technique is examined. Two practical examples are studied to show the capacity of the new lifetime and quantile regression models.
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    Modified-Lindley distribution and its applications to the real data
    (Ankara Üniversitesi, 2022) Kuş, Coşkun; Korkmaz, Mustafa Çağatay; Kınacı, İsmail; Karakaya, Kadir; Akdoğ, Yunus
    In this paper, a new three-parameter lifetime distribution is proposed by mixing modified Weibull and generalized gamma distributions. The point estimation on the distribution parameters are discussed through several estimators. The interval estimation is also studied with two methods based on asymptotic normality and likelihood ratio. A Monte Carlo simulation study is performed to evaluate the biases and mean square errors behaviors of point estimates for a different sample of size. A simulation study is also conducted to investigate the coverage probabilities of confidence intervals. The distribution modeling analyses are provided based on several real data sets to demonstrate the fitting ability of the introduced distribution.
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    On a unit-EEG quantile regression analysis
    (CRC Press, 2025) El Moustapha Sidi, Mohamed; Kuş, Coşkun; Kokmaz, Mustafa Çağatay; Pekgör, Ahmet; Karakaya, Kadir
    Many statistical distributions have been introduced in the past two decades. However, offering distribution with unit domain is becoming popular and quantile regression analysis is provided to demonstrate the applicability of introduced unit distributions. Unit distributions are used for modeling the recovery rate, mortality rate, proportion of the educational measurements, etc. The distribution with bounded support can be used for modeling the lifetime data. A failure time distribution with upper limit does not mean that all failures in a life test can be observed. From an engineering point of view, the bounded lifetime distribution is more appropriate than the lifetime distribution with infinite support because life is always finite. There are many practical situations that lead to bounded support in the areas of lifetime study and reliability engineering. For example, when failure or reliability life test data is collected by an automatic recorder, the lifetimes below L and above T (L < T) may not be measured at all due to the device’s resolving power or other environmental influences (Mang and Xie 2011). From this perspective, new distributions with bounded support such as the Beta or Kumaraswamy distribution are required for modeling such lifetime data. https://www.taylorfrancis.com/chapters/edit/10.1201/9781003379881-14/unit-eeg-quantile-regression-analysis-mohamed-el-moustapha-sidi-co%C5%9Fkun-ku%C5%9F-mustafa-%C3%A7a%C4%9Fatay-kokmaz-ahmet-pekg%C3%B6r-kadir-karakaya
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    Parameter estimation procedures for log exponential-power distribution with real data applications
    (Adiyaman University, 2022) Korkmaz, Mustafa Çağatay; Karakaya, Kadir; Akdoğan, Yunus
    In this study, some estimation techniques are investigated to estimate two parameters of the log exponential-power distribution. The maximum likelihood, quantile, least squares, weighted least squares, Anderson-Darling, and Cramer-von Mises estimation methods are studied in detail. The efficiency of these estimators is validated through Monte Carlo simulation experiments. Also, four real data applications are performed and Kolmogorov-Smirnov statistic results for all estimators are presented.
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    The two-sided generalized lomax distribution: Estimation and application
    (CRC Press, 2025) Karakaya, Kadir; Akdoğan, Yunus; Korkmaz, Mustafa Çağatay; Şahin, Fatih
    The two-sided generalized lomax distribution: Estimation and application. https://www.taylorfrancis.com/chapters/edit/10.1201/9781003379881-16/two-sided-generalized-lomax-distribution-estimation-application-kadir-karakaya-yunus-akdo%C4%9Fan-mustafa-%C3%A7a%C4%9Fatay-korkmaz-fatih-%C5%9Fahin