Browsing by Author "Arslan, T."

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Alpha Power Maxwell Distribution: Properties and Application
(University of Guilan, 2021) Erdogan, N.; Bagci, K.; Arslan, T.; Celik, H.E.
In this study, alpha power Maxwell (APM) distribution is obtained by applying alpha power transformation, a reparametrized version of the Exp-G family of distributions, to the Maxwell distribution. Some tractable properties of the APM distribution are provided as well. Parameters of the APM distribution are estimated by using the maximum likelihood method. The APM distribution is used to model a real data set and its modeling capability is compared with different distributions, which can be considered its strong alternatives. © 2021 University of Guilan.
An Extension of the Inverse Gaussian Distribution
(World Scientific Publishing Co., 2022) Arslan, T.
In this study, an a-monotone extension of the inverse Gaussian (aIG) distribution is introduced. Then, the method of moments estimations for the parameters of the aIG distribution is provided. A real dataset is used to show the fitting performance of the aIG distribution. The results show that the aIG distribution fits the corresponding dataset better than the IG distribution if the well-known goodness-of-fit statistics are taken into account. Note that the aIG distribution is defined as a general class of the IG distribution by adding a new shape parameter. It can be considered an alternative to the IG distribution in modeling data from different areas of science. © 2022 by World Scientific Publishing Europe Ltd.
A New Family of Unit-Distributions: Definition, Properties and Applications
(Turkic World Mathematical Soc, 2023) Arslan, T.
In this study, a new family of unit-distributions is introduced. Then, a unitGumbel distribution, member of the proposed family of unit-distributions, is obtained as an example, and some of its statistical properties are provided. The maximum likelihood method is used for estimating the shape parameter of the unit-Gumbel distribution. In addition, a new family of continuous distributions is defining by using the composition technique. Finally, real data sets are used for modeling purposes. The result shows that the unit-Gumbel distribution is preferable over some well-known unit-distributions such as the beta, Kumaraswamy, and Topp-Leone, and also the unit-Gompertz distribution, which is recently introduced.
On the Maximization of the Likelihood for the Generalized Gamma Distribution: the Modified Maximum Likelihood Approach
(Springer Science and Business Media Deutschland GmbH, 2025) Arslan, T.; Acitas, S.; Senoglu, B.
Maximum likelihood (ML) estimation of parameters of the generalized gamma (GG) distribution has been considered in several papers, and some of them stated that the ML estimation has some computational difficulties. Therefore, different approaches including numerical methods have been proposed for the ML estimation of parameters of the GG distribution. However, it is known that using numerical methods may have some drawbacks, e.g., non-convergence of iterations, multiple roots, and convergence to the wrong root. In this study, we rehabilitate the ML procedure via the modified ML (MML) methodology and obtain the likelihood equations in which two of them have explicit solutions, and the remaining one should be solved numerically. Since the MML methodology explicitly solves two of three likelihood equations, the mentioned drawbacks are alleviated. We also propose a simple algorithm to obtain the estimates of the parameters of the GG distribution. Then, the GG distribution is used for modeling the real data sets, and the performance of the proposed algorithm is compared with the Broyden–Fletcher–Goldfarby–Shanno (BFGS) and Nelder–Mead (NM) algorithms. The results show that the proposed algorithm is preferable to the BFGS and NM algorithms in terms of computational sense when considering the GG distribution. © The Author(s) 2025.
The Unit-Cauchy Quantile Regression Model With Variates Observed on (0, 1): Percentages, Proportions, and Fractions
(Hacettepe University, 2025) Arslan, T.; Yu, K.
In this study, a new parametric quantile regression model is introduced as an alternative to the beta regression and Kumaraswamy quantile regression model. The proposed quantile regression model is obtained by reparametrization of the unit-Cauchy distribution in terms of its quantiles. The model parameters are estimated using the maximum likelihood method. A Monte-Carlo simulation study is conducted to show the efficiency of the maximum likelihood estimation of the model parameters. The implementation of the proposed quantile regression model is shown by using real datasets. Quantile regression models based on unit-Weibull, unit generalized half normal, and unit Burr XII are also considered in the applications. The application results show that the proposed quantile regression model is preferable over its rivals when several comparison criteria are taken into account. In addition, the fitting plots indicate that the proposed quantile regression model fits extreme observations on the right tail better than its strong rivals, which is important in quantile regression modeling. © 2025, Hacettepe University. All rights reserved.